1. In general, build your race and choose tech specializations to fit as many modules into a ship as possible.
2. Early game, focus on economy and tech.  Start researching Carrier tech when you think the AI will declare war in ~50 turns.  (You might be able to delay war preparation a bit longer if you're not afraid of losing a few starbases and outer colonies.)
3. Start with a Cargo/Large/Huge hull.  Add Engines and Life Support to taste, and as many Hangar bays as you can fit.  Ignore weapons, armor, etc...
4. You can start building those carriers now.  Your fighters will automatically pick up the new tech (see next step) after a while.
5. Research better weapons.  Prefer to go deep into one branch (e.g. Beams) rather than spreading wide.  Prefer weapons over countermeasures (armor, shields, etc...).
6. Research enough logistics to fit 4+ carriers into your doom fleet.
7. Build more doom fleets (and invasion fleets)
8. Watch the galaxy burn.

Assault IIRC