* Don't send more than 25 ships to any star. More than a 25 ship advantage does nothing for you.
* Spread your ships across all stars in the vicinity when they are neutral.
* Attack the AI early if you can. Don't wait to be attacked.
* Attack from several directions at once. Sending ships from one star is pointless, but 3 stars at once? Progress!
* Try to choose a starting location that's farther away from enemies, or close to only one enemy (that you can rush early)
* Always go after positive stars first (asteroids, gas cloud, comets, etc)
* Leave crappy stars for the AI (purple anomaly is great because AI can't send ships from there quickly enough)
* Think strategically about chokepoints. Don't take stars that you know can be attacked from 3 sides. Go after a star that can only be attacked from one side.
* When you have a lot of stars, turn off production on the far-away stars by tapping/clicking on them (this removes the arrow). This makes ships get created closer to the front lines.
* Send ships in a patrol route. Don't pile them on one star. If you have a perimeter, make them go around in a circle. It's better for defense.
* Speaking of defense, if you are getting attacked, cancel the star's ship redirection (click/tap on a star). This gives you a pretty hefty 30% defense bonus for all ships there.
Feel free to add any other tips.