1) Pick your weakest, closest neighbor; preferably one you hate.
2) Build a fleet that can shoot down any troublemakers.
3) Stage transports around all of their worlds.
4) Declare War / Invade as many planets as possible in one turn before they can react.
5) Build up captured worlds.
6) Repeat on next-smallest / least favorite neightbor.
It's really all about being a bad neighbor.
* If you haven't already, capture all the Minor Race planets that you can before going after Major Races.