You will get tokens when you win a battle. Use these to upgrade rooms, and hire new crew members from home planets (Earth and Norfoo).
You can assign your captain to any job: he doesn't have to work in the bridge. But watch out: you'll get a Game Over if he dies in battle.
Make sure that your ship and crew are in top condition before moving onto a new planet or galaxy - very often a new fight will await you on the other side of warp! Make sure all of your crew have a full health bar, and stick them in the medibay until they're at maximum health.
Each weapon in the game has a mini-game associated with it. When firing the first missiles you gain, you need to tap each of the circles in the right order, just as the orbiting sphere hits the tip of each circle. To fire your awesome space-machine guns, you need to tap the screen just as the orbiting sphere passes through each dot. This latter game gets much faster with each orbit.
Always be aware of the position of each and every crew-member, and what they're currently doing. Once they've completed a job, make sure they go back to their designated room to carry on their normal duties.
Your engineers can actually make repairs to the ship! If a fire has broken out, or there's a hole in the side of your spaceship, make sure you dispatch your engineers to address the problem. Simply tap on them, then tap near the damaged area to have them move out and do some serious welding.
Upgrade rooms and crew pretty evenly, so that the increased power of each one compliments the other. As a general rule, and if you can use any token to make an upgrade, spend the token type that you have the most of in your bank.
Your Dodge Generator requires ammo tokens in order to be effective. Always keep one of these in the bank so that you can at least avoid the first volley of your enemy, and get a decent shot in yourself.