Without going into to much detail, some quick tricks are.
 
 -Focus on nothing but factories on your homeworld at the start.
 -Build a cheap colony ship that you can use as a pop transport from your higher production planets that can build pop faster to the newer or less manufacturing based planets.
-New colony's, no matter what you want to do with it later build factories at the start until it gets more pop or has stabilized.
-Dont neglect the Power matrix improvement, it can give +2 manufacturing to near by factories.
-Dont be fearful of sending out a colony with even as low as .5 pop early on. that way you can keep the home world production high and just transport more pop over to them later.

-If your going evil then focus on the line that gives +production bonuses to all planets first. Tho you dont HAVE to do it, it can be a nice boost.
-and if you really want it easier, get the prolific ability that doubles the pop of all new planets you colonize

The yor, or synthetic in general are slow to start but then become a powerhouse and can rocket ahead really fast. Once you get max pop on each planet the raw production can be huge compared to other races.

Im glad i could help Good luck and have fun!

A general synthetic vs biological question

Comparison

ability                           synthetic                biological
pop. growth(max)          2.0/turn                  0.3
automatic growth             no                        yes

So as synthetic you can chunk out people almost 7 times
faster than any biological species.
For what would you need this amount of people?

1) Income [Wealth, Manufacture, Research]

The formula for total production is
tp = 2*p^0.7.  With p being the population count in
Billions.

After 25 Billions you get to the point of deminishing returns.
If you get to 31 Billion you only get 2 points in total production.
Considering falling happiness its not really worth going beyond
25 BP.

2) Population growth

here comes the population growth. With biological species you
would need 22/0.3 = 73 Turns to get 25 Billion people (BP) .
I assume you had 3 BP with you colony ship.

With synthetic about 19/2 = 10 Turns. Considering you've got
6 BP on your colony ship.

3) Invading planets

Invading planets sucessfully is very easy in GC 3.
In fact with max. 3 BP of invaders you can take over pretty much
every planet even considering the highest amount of planetary defenses.

In GC 2 you needed twice the amount of invaders compared to
planet population. For a 16 BP world 32 BP of invaders would be
needed. With biospecies 32/0.3 106 Turn for 1 planet are needed.
Or even 10 Turns for 10 Planets.
Witch synthetic, and 10 planets you can get the number in 2 turns.

4) Major drawbacks

Manually increasing population
and distributing them to other colonies

Manually increasing population: What is almost automatically done with
biological species (you only need 1 Fertiliy booster building on
each planet) is very tiresome with synthetic beings.

distributing them to other colonies

This is the major problem in my opinion.
It is very time consuming.

considering manufacturing ability.Only few planets are able to generate
population in reasonalbly fast rates.

The amount of work, transport ships, ...  scales with amount of planets.
What is manageble with 5 Planets on small map will be overwelming considering
you have 50+ planets.

Conclusion: Stardock needs to implement a autogenerate + distribution funcionallity,
To lower micromanagemt an a large scale.

throu buildings. Like linking planets to starbases you need to link planets

to planets and set population transfer rates.

Or even transport routes much like trade routes.

At least thats my opinion. I don't play with synthetic on maps bigger than small.
Due to the fast increasing amount of micromanagement involved with synthetic beings.

Afaik synthetic can grow at 6/turn, not just 2.  The advanced assembly techs are mid-late game, but they are very very fast.  

I would have to disagree about the transportation mechanic other then the initial colony ive never used a transport to move people 

the first things i build are 2 factories after that if the approval is high enough to support more population it only takes about 1-2 turns

if i had some weird mechanic like -95% to production You could always rush buy

Synthetic races should automatically build transports and colony ships with the population already in them.  It would take the same amount of time as building them both manually but it would cut down on the micromanagement.

While I agree it maybe should be looked at, I think people forget it is a race ability. And it kinda should be stronger then most races by default. Otherwise what's the point of the ability