Basic strategy: You should always be building a colony ship and have a colony ship onits way to colonize a system.
At the beginning of the game, you can easily use colony ships as scouts. Compared to other space games, colony ships are ridiculously cheap. If one gets attacked and killed, it is a small loss. But if it gets through, you have a colony that much more quickly.
Colonize every planet in sight. But don't colonize planets in systems with AI colonies until you have a treaty with them. If you don't have a treaty with them and colonize the system, it will make them mad, and they might not ask for a treaty. Once you have a treaty, it will still make them mad. But who cares, you have a treaty with them.
Don't accept military alliances with races that colonize the same planet types until you have first built colonies on all those planets.
At the beginning of the game, build mostly fighters and/or mines. Since they don't cost any maintenance, they don't slow your expansion. I like to build units--fighters--at every colony that has already finished building its max number of facilities.
Use transports to move fighters across wormholes and assemble a lot of fighters on the three or so wormholes leading into your empire.
Did I mention expand, expand, expand and always have a colony ship on its way to a new colony?