The basics of this are summarized pretty well in this guide:
http://steamcommunity.com/sharedfiles/filedetails/?id=161168470
I.e. make 2-4 scout frigates first, then 2 colony ships (summarizing colony frigates and colonizer capital ships). The rest depends on your faction and your position relative to your teammates.
In the aggro position and if you are not Vasari, the next step is the production of as many light frigates as your fleet maximum allows. Then you need a laboratory in order to increase your fleet supply and spam more LF, and that's already where the opinions of experienced players diverge. I personally prefer a military lab because this will let me purchase the level 1 hull and damage upgrades before I build the 2nd laboratory, but I'd like to discuss whether that is too early. Another pro for a military lab is that it lets you research additional ship types more quickly and cheaply if you need to counter long-range frigates, starbases or corvettes in the early game. In some games you will even want the military laboratory for a titan before getting any civic research stations. Repair platforms can also be very useful so I suggest military labs for aggro or death spot players.
Other players will prefer civic research stations in order to colonize key planets (which is especially useful against Vasari because it slows down their starbase construction/upgrades) or to improve their economy, and if they are Advent Rebel, to get the resurrection researches sooner. Researching Arctic/Volcanic/whatever occupation just for economy ist not viable in my opinion, though, because a good opponent who puts his resources into his military will most likely take one of your planets before the economic research pays off, thus negating your economic advantage while maintaining his military superiority.
Note that you will need some resources to upgrade newly colonized worlds between all the frigate spam. When playing with the conventional settings, in particular with quick start and faster income, you will be able to colonize&upgrade 2 asteroids as soon as your colonizers arrive and also purchase your first fleet supply upgrade around the same time.
After you have fully used your fleet capacity, it's time to upgrade it again. Like I said, I will upgrade my hull/damage and, if I'm Advent, shield points at this time in order to postpone the fleet research's income reduction while still increasing my military might, but I'm not sure whether one should just continue spamming frigates. This might also be a good time to research carriers (if you are facing starbases), flak frigates (if your enemy is using corvettes), long-range frigates (if you can hide them long enough to get a sufficient amount and if the time before your opponent counters them with corvettes/fighters will be enough for you to take a planet which is worth it), starbases (if your opponent is somehow superior, e.g. because he's getting feed and you are not or if you are being doubled), Siege frigates or another capital ship (in the opposite case) or maybe other stuff which I'm not aware of atm.
One could write much more about non-aggro positions and games with Vasari, but I'm not going to do that right now ^^
