Noob questions

You build additional modules on your starbases by sending more constructors to them.  Each constructor can add one module.  It's an inefficient system, but it's what we've got.  TA also has the starbase module queue system, so you don't have to cherry pick your upgrades, but I haven't tried that yet.

As you research up the factory/production tree, additional modules will be unlocked that you can add to mining starbases via the above mechanic.  The initial mining is done when you construct a starbase on the resource, and gives you a 5% bonus of that resource type (military rating, influence, economics, morale, and research).

Of the ships that you start with, one is a "space miner" that can construct asteroid mines on asteroid fields that provide the planet to which they beam a minimal to moderate amount of industrial production (which decreases with distance).  If you click on the miner itself and set it to auto, it will go around and build them automatically, albeit not in the most useful order-it will build the first level on all available asteroids before it builds the second level on any.  However, space mining as a whole is generally not worth researching up to and completing, so this is a flaw that can be largely overlooked.

Thanks, I really appreciate the help, this is the first time I've played a strategy  game like this and have been somewhat confused.

Make sure you build space defenses and weaponry, otherwise you have to post a fleet/ship to guard the thing. And god help you if you forget to order the ships to attack the enemy and your star station is unarmed *explosion noise*