Welcome, welcome, newcomer. I have a lungful of advice, and most of it's wrong, but I hope it helps anyway. 
1). Figure out who you like to play! Do you like having a big, sturdy fleet with few synergies, strong early-game options, the best repair units around, and strong economic support? Play TEC! Do you like having a fleet with several synergistic options, really sleek and well-designed units, and the ability to field a nigh-impregnable "battle ball"? Play Advent! Do you like having missiles that can jump through shields and an absolutely insane late-game strategic advantage? Play Vasari!
2). Figure out the basic procedures: what to build when. For starters, I build a capital ship factory right away (so I can get my free capital ship ASAP!), and get my extractors up and running. I immediately build scouts (2-4 depending on the size of the system) and send them on their merry way. I build light frigates and a colony frigate, and begin clearing out the locals, using my light frigates on lightly defended systems, and using my capital ship on the heavier garrisons. At the same time, I build a pair of civic labs so I can learn to colonize ice and lava planets (which are ALWAYS right next door, for some reason >.<) as soon as possible.
3). When doing research, learn what gives you the most bang for your buck, when. There are a truly mind-numbing array of research options out there, but some of them are more important than others at different stages of the game. For example, that 5-10% extra metal or crystal you get at tier 1 won't count for as much in the early game as the ability to colonize volcanic and ice planets, which will give you more money sooner; but in the late game, when you have a huge number of metal and crystal (and a large fleet chewing up your income), that 5-10% might mean the cost of an extra ship every second! By comparison: trade stations are great, but not when you only have three colonies! They're better when you have five to eight.
Remember, though: your research course will ALWAYS vary depending on how close your opponent is, what strat you're pursuing, and what your neighboring planets are like. If you don't need ice and volcanic research immediately, don't get it! Victory, in this game, is dependent on doing the right thing at the right time under the right circumstances. If there's a pirate base between you and your opponent, then you can relax a bit and build your economy. But if you're right next door, grab the most powerful capital ship you can get and prepare to fight, fight, fight!
4). Learn the armor and damage types, so you know which units affect which units best. I'll even be a nice guy and outline them (from memory ) here:
- Fighters: These guys do great damage against fighters, bombers, siege frigates, and long-range frigates; they're less than spectacular against anything else. Important note: they're great for destroying trade vessels (destroying which reduces enemy productivity for 25 seconds)
- Bombers: Bombers do great damage against structures, heavy cruisers, and, in numbers, against capital ships.
- Damage Type: Anti-Very Heavy
- Light Frigates (Cobalts, Ravastra Skirmishers, and those Advent thingies that look like killer tuning forks): they do great damage against flak frigates, support cruisers, and light carriers, but they take heavy damage from long-range frigates (LRFs) like the Illuminator, Javelis, and the Kanrak Assailant. They all get an anti-caster ability that can help neutralize support cruisers that use abilities, but good luck getting them near a well-defended fleet without heavy support!
- Armor: Medium
- Damage: Anti-Heavy
- Long-Range Frigates (Javelis, Illuminator, and Assailant): They tear through light frigates, but they take heavy damage from Fighters (not Bombers!), scouts, and heavy cruisers.
- Armor: Light
- Damage: Anti-Medium
- Siege Frigates: Though they can bomb planets early on, they do very little damage, and take extra damage from fighters and scouts and heavy cruisers. Don't use them! If you want to bomb something, use capital ships.
- Armor: Light
- Damage: Anti-Heavy
- Anti-Strikecraft Frigates (the Garda Flak Frigate, the Advent Defense Vessel, and the Junsurak Sentinel): these guys are designed to knock out fighters and little else; but they can only be really effectively destroyed by Heavy Cruisers and Light Frigates.
- Armor: Heavy
- Damage: Anti-Very Light
- Support Cruisers (the Hoshiko, the Cielo, the Stilakus Subverter, the Severun Overseer, the Iconus Guardian, and the Domina Subjugator): these are your "caster" cruisers: they exist use abilities. They are all vulnerable to light frigates and heavy cruisers. They take slightly reduced damage from fighters and long-range frigates.
- Armor: Heavy
- Damage: Anti-Heavy (but they do very little damage -- 125% of very little is still very little )
- Light Carriers (the Percheron, the Lasurak Transporter, and the Aerie Drone Host): these guys also take additional damage from light frigates and heavy cruisers; they take slightly reduced damage from fighters and long-range frigates.
- Heavy Cruisers (the Kodiak Heavy Cruiser, the Destra Crusader, and the Skarovas Enforcer): These bad boys do increased damage to everything but light frigates, and take vastly reduced damage from everything but bombers. Don't think that makes them invulnerable, though!
- Armor: Very Heavy
- Damage: Composite
Important Note: Some ability descriptions, as well as the score screen, will refer only to frigates without referring to cruisers. DON'T PANIC! As far as the game is concerned, cruisers are frigates.
5). My last piece of advice: very carefully look through the score screen! It can tell you a lot. If you see a lot of "Credits lost to planet underdevelopment" or see your opponent gaining lots of money in a category you're not seeing gains in, ask people on the forums what's up. The answer may be simple ("Oh, don't worry, the Advent are just good at gaining money that way"), or it could be that you're ignoring something. Fear not! We won't bite.
