Here's a short custom walkthrough, just for you! This is a Dreaded Build Order, which you will of course completely ignore once you have a few wins under your belt. I know from experience that this'll beat 4 lock-teamed hard AIs (if played a touch more defensively), and I'm trying it against 7 right now. Not necessarily great against a human, but it should get you started.
Ok, this will assume you're Vasari, since I'm at work and it's the only side I know well enough do talk about without looking stuff up. Most of this works for all the others, though, so feel free to adapt it.
Note: you can pause the game at any time to have a look around and even give orders. Orders don't show up in pause, so if you want to make sure everything went through ok just un-pause for a moment, then pause again after each order. Good for getting those early orders done, or for selecting enemy targets in a battle.
0. Do the tutorials. They are Buff.
1. Set yerself up a 1v1 map, but pick one of the larger ones. The AI is not very good at expansion, and a larger map will give you more time to develop before the enemy arrives. Check the AI's difficulty (the little rank symbol at the end of the player selection screen, just before the game starts) - it defaults to Average, and you might want Easy for a game or two. Following this should guide kill even an Average pretty easily, though.
2. Early crystal is tasty delicious! First thing to do when you come into the game: go to the Black Market (that is, hit the pirate button at the top of screen, and then the Black Market button to the left). Buy two lots of 100 Crystal - it costs 300 credits to buy the first lot, and 350 to buy the second. Make sure you're not SELLING crystal. That would be bad.
3. Right, now you need to go to your home world, click on the Civilian Structures icon (the cog in the main planetary menu), and build a Capital Shipyard and a Crystal Mine. You've got two builders, so they can only start on two things at once anyway.
4. Thanks to the extra crystal, you can also afford an upgrade the civilian infrastructure on your homeworld (back in the general planetary menu, click on the green world icon). That gives a pretty huge amount of credits as the game goes on.
5. Build an explorer (again, back to the homeworld's main menu, click on the yellow frigate builder button). If you did all this fast, or were using pause, you should now be out of money.
6. ...but that's ok, since your first capital ship is free. Go to the capital ship yard (which is still building) and ask for an Evacuator. It's not the best against human players, but is decent against the AI and it makes life much easier later on since you don't have to mess about with colony ships.
7. In a moment you'll have enough for a second scout ship. As the two scouts get built, just set them to auto-explore (right click on their explore icon). Note: later on you may find some un-colonisable systems with resources in them. As Vasari, your scouts can capture these for free - just turn off auto explore and park them in the area (assuming there are no defenders). They'll take them eventually. Non-Vasari people can do the same with Colony frigates.
8. Build extractors in your home system for the rest of the asteroids there, as you get money for them (250 credits each).
9. The capital ship: get the colonisation ability as your first ability. Later you'll want the other 2 powers, pretty evenly (just leave colonise at 1). Both are for killing enemy capships, so take them off auto-cast as you get them and use them manually when required. Nano-disassembler is for killing capships, and Gravbomb is for stopping wounded ones when they are about to jump away. Remember that capships don't have as much firepower as an equivalent cost of frigates. Can't stress that enough. Capships are for their abilities, frigates are for killin'.
10. Having said that, your capship alone is enough to take out the average asteroid defences (if very slowly), so go kill one nearby the moment your ship is built. Take colonise OFF auto-cast before you do, though - you want to clear the enemy forces first so they don't bomb the colony the moment it's built. Once they're toast, colonise that sucker.
11. Scrap your capital shipyard! You're not going to need it for a long time now, so you might was well put those resources to work and free up a precious orbital slot. Skip this stage if it's too much of a pain in the bum, though - you are going to need to rebuild it some day anyway. To scrap, go to the shipyard, and hit the skinny yellow button under its picture at the bottom of the screen, and wait a while.
12. Note that, back home, you haven't built ANY combat frigates yet. That's because your skirmishers are Teh Suck. Instead, build a single Weapons Support Centre (military lab) as soon as you can afford it.
13. ...and research Assailants. They are your long range missile ships, and they specialise at killing frigates. Since frigates are your main enemy at the moment, this is a good thing to kill.
14. As you can afford it, build Assailants all the way to your population cap. You are going to need to delay on occasion to build basic colony stuff (see #15 and 16), but this is pretty urgent. A full fleet of Assailants are pretty buff. Put them ALL with your capital ship (set the rally point to the capital ship, if you don't know how let us know). If you are a bit short on crystal, feel free to build a Skirmisher or two - they do suck a bit, but they're very tough and make decent meat shields.
15. New colony? You must must MUST get the civilian infrastructure in the black - colonies start out by bleeding your credits dry. Asteroids are easy, since they only need one level of Civilian Infrastructure to break even, but planets need two levels (more helps, but until they get two they are actually costing you money). Get those done asap. Second thing to get is to fill all the extractor slots. Then worry about trade ports, defences etc depending on location, and not until later in the game.
16. Pirates are your friends! Go to the pirate screen (the button at the top of the screen, then use the buttons on the left to go to Pirate (the other option being Black Market that you used earlier)). You WILL be winning the first bidding war. In fact, you should win most of them. Make sure the enemy has more bounty than you - that's all you need to do. When you hear "pirate raid imminent" get ye to the pirate screen and WIN. Don't go more than a bid or two above the other guy, but watch like a hawk and up his bid the very moment he makes yours higher. Remember the black market! Use that to sell stuff (generally metal) to make sure you have another 250 creds to bid, and another, and another, until you win. The pirates should be almost winning the game for you. Don't lose them! If you do, see #17 and 18 below.
note that you can, at any time, go to the pirate screen and check how big the "pirates are a comin'" bar is at the bottom. They'll come killing stuff when the bar is full.
Note also that, as your target loses stuff his bounty will go down. That doesn't effect a pirate raid once it's been launched, but 1. it does let you see if the pirates you sent are doing damage, and 2. it means you shouldn't put a bounty on the enemy too early - otherwise *you'll* win bounty by killing his stuff, making his bounty go down. Wait until the attack is imminent, and bid then.
REMEMBER THE BLACK MARKET. You should (almost) never lose the bidding war.
17. Fightin'. First, focus fire. Easiest way to do that is to grab the whole mass of your fleet. Then look at the contested system in the Empire tree on the left of screen. notice all his ships lined up on that view? Right-click your fleet against one ship, then shift-right-click each ship in order. Your entire fleet will then slaughter one poor bastard, then the next, then the next. Since he will spread his damage around, while you are reducing his firepower with every kill, you will win any fight that's even close to even.
Remember to target frigates first, especially enemy long-range frigates (like the ones you are using). Capital ships go last. The only exception is if there's a fairly damaged one trying to retreat and your Evacuator has it's gravbomb. In that case, and only when they turn to retreat, it can be worth it to target everything against that capship and gravbomb it to stop it getting away.
Particularly for early fights, confound the enemy. Watch your fleet selection in the Empire tree on the left, and see when one of your guys come under attack (they'll flash red). Wait 'till their shields go down (that's the little redish bit, not the blue bit), it's time for the Dance of the Happy Dodge. First, move to the OTHER SIDE of the enemy force - it takes ages to turn but it's fast to speed up straight ahead, so your ship will quickly zoom through the enemy attackers. They can't hit stuff behind them, so they'll slowly turn around (while your forces keep pounding them. Now zoom back a bit, shift-right-click on the nearest system to the retreating unit, and shift-right-click a second time on the system you're fighting in. That'll mean your escaping ship will usually come back through your fleet - though this will often mean taking a second lot of damage as they go through the enemies as well - and then they'll jump out. As soon as they get to the other side they'll turn around and come back. The AI targets the nearest enemies, not the most damaged, so your wounded guy will usually be able to fight on as normal.
At least in small battles, you really shouldn't lose any ships. Don't over-react, though - make sure there's a lot of enemy ships hitting your one before you run away. Sometimes it's just one or two, which you can ignore.
18. Defending. The AI, both pirate and regular, utterly sucks against defences. It'll blunder straight into them and almost never bothers to go look for an easier system. So if you know where the enemy is likely to attack, build a dozen gun platforms right on top of each other, in a string that covers the edge of the planet closest to the enemy, and, if you're feeling especially mean, a pair of repair platforms (you'll need to research it). That'll beat almost any fleet the Pirates or a single AI can throw at you - yes, without any defending fleet at all. During the battle as you lose platforms, just re-build them right behind the current ones - the AI won't stop you (it'll keep hitting the closest target), and you can keep that going as long as it takes the AI to die horribly. It generally takes more than one AI to beat such a defence, and it'll beat even an end-game maximum level pirate attack (assuming you have missile / armour upgrades by that late stage).
Don't bother with hangers - turrets are crazy good and the AI doesn't build enough fighters / bombers to bother you. The AI is also to silly to go around turrets, so siege frigates will happily park right inside your guns to bomb the planet, as long as you correctly predict the direction they're coming from (rarely difficult).
Once your more established you're going to want to upgrade pretty much everything on every planet to maximum, apart from bombardment defences and tactical slots / turrets - generally, you only need those on frontline systems.
19. Onwards and upwards: you can survive a long time on just a nice compact chainsaw crew of Assailants. When you get a chance, especially if early and always if the pirates have just gone into a different system, go into enemy systems and annihilate anything in orbit. Oh sure, bomb it with your Evacuator if you have time, but a general slaughter of structures is always worthwhile. Remember from 17 - you should win any even fight against the AI, so if they turn up just get out of turret range and tear them up.
20. More fleet - get ONE level of fleet supply upgraded (each level really hurts your economy, so keep it as low as you can). It might be worth getting a second capital ship now, but against 1 AI it's probably not. Just pile up the frigates. Once your Evacuator hits level 6 it'll bombard pretty nicely, but if you're in a bit of a hurry it's worth either a second capship or some siege frigates. Also research your phase missiles upgrade - it improves both your Assailants and your missile turret defences, the two units doing almost all your fighting.
21. Research: Anyway, all of that means you don't need more than 1 military lab for a while. Your next objective is Ice and/or Molten world research (depending on map) at the 2nd level of civilian tech. Do this fairly quickly and you'll find yourself with a large part of the map before the computer gets up much steam.
22. Trade Ports (whatever it's called as Vasari) are your next objective at the 4th level of civilian tech. EVERY planet and asteroid gets a trade port. If you got a few colonies then improving your resource rate is worth getting, too, and Refineries are decent. You get all of that at level 4 civ tech.
23. If the game is still going (and really, you should have walked over a single AI by now), you're going to need to buff your fleet. Get to the 4th level of Military tech and get your Assailants' AOE attack (you'll need to research flaks, too, though you'll rarely need them). You now have a stupidly awesome flying chainsaw that also does area-of-effect attacks, perfect for carving through enemy swarms. Upgrade their missiles some more, too, and get another fleet supply upgrade (I don't like more than about 3 until you've finished step #24 below - remember that each upgrade to your supply really hurts your economy, and the Flying Chainsaw is perfect for action as a small, outnumbered fleet - just not TOO badly outnumbered, so yeah, get to level 3 supply as you can afford to fill it). If you do get a second capital ship, I like the bog-standard battleship (the first option). At level 6 it gets a massive area-of-effect damage booster, and with your assailants that means OUCH.
Oh, you'll probably need some culture by now - if you see phase lanes changing colour it means the enemy is going for culture, so research cultural techs and plonk a broadcast centre on most planets.
24. Game STILL going? It's time for the Vasari trump card: go for the end of the Civilian tech tree. Get phase gates, and put one on pretty much every planet you have. That lets your fleet run around defending you, if things are grim, while you complete the teching up. Then go right to the end and get Returning Armada. That fills your fleet popcap with an assortment of frigates and cruisers for free. Yes, for FREE. Throw whole fleets on massive kamikaze assaults if you like. Spend all your dosh on research and defences, and then pump that fleet popcap as high as you like. Your only issue will be assembling those vast fleets and throwing them in the general direction of the enemy.
For end-game I like two main combat fleets, each with 2 capital ships leading (the battleship to do the AOE blast, and the Evacuator to bombard / colonise planets and trap retreating cap ships - maybe get a third capship in each fleet if you want to kill planets faster). It can be worth getting a siege frigate force of a dozen or so, but get them before your returning armada kicks in, or it can be a pain to build them before the popcap gets refilled. Then have a couple of mop-up fleets of 10 ships or so, just to help guard new colonies while they get on their feet. Build maximum defences in each system as you go - remember, you aren't buying ships so you generally have heaps of money.
Win.
Summary of early game (anti-AI only):
Buy 200 Crystal
Capital shipyard
Crystal Extractor
Civilian infrastructure for homeworld (Terran starts only)
2x Scoutships
Evacuator
All other Extractors in starting area
Weapons lab
Research Assailant
Build Assailants to popcap
Colonise planets as available (each gets 2x Civilian infrastructure, all extractors)
Build defences on choke points, as required (4x turrets early game, 10+ turrets and 2x repair platform later on, with a phase gate and nanite defence as the techs become available, much later)
Increase supply one level
Build Assailants to popcap again
Research phase missile upgrades
Go to level 4 Civ tech
Research and build trade ports
Research resource upgrades, refineries
Go to level 4 Mil tech
Research Flak frigates -> AOE attack for assailants
Research phase missile upgrades
Go to level 3 supply -> fill fleet with Assailants again, second capship
Research and build Culture
Go to level 8 Civ tech
Phase gates -> Returning Armada
Research anything that looks worth having, then more supply, couple more capships, lots of everything
Win
Note with Assailant (since I love them so): their AOE attack is a toggle. That is, once they turn it on they can't move, but get extra range and hit enemies next to their targets. Don't worry about turning them on or off manually - they'll work it out (usually). Be careful, too - when it's toggled on it looks a lot like when it's toggled off, so if you are trying to do it manually pay close attention. Also, Assailants occasionally decide they don't want to switch the big missiles off despite your frantic movement orders, so sometimes some will get left behind during a retreat. Feel free to hit pause and toggle them off manually if you see a group staying behind.
Note with supply: once you've got near-maximum supply, even with a huge empire, you're going to be fairly short of cash. As always, keep supply as low as you can reasonably get away with. Massive amounts of money means you can take a world, and stack up a full build.