Hi!

With a miner ship. Since it takes a long time to upgrade to higher levels, you my find usefull to have more miners present. My rule of thumb is 1 miner for every cluster of asteroids I have.

BR, Iztok

The "time to upgrade" is the number of weeks the miner will have to stay on the asteroid before you get the effects from the mine (5 weeks is the first one). Its not like a star base that you'll see it done on that move. After you have mined you'll need the other techs that Alexander mentioned. If you don't have the additional mining techs, your miner will be dormant unless you move it to another asteroid. They move very slowly, so as Iztok said, its best to have one per cluster. Later it will take 10 and then 20 weeks to get the later mining upgrades so you may even decide to have multiple miners for the same cluster. Those techs are pretty expensive in research time though. (and AI's dont like trading them)

Yes, the distance to the target planet effects the bonus that planet will get. its best to assign the asteroid to the nearest planet. After the mine is complete, you can click on it and it will tell you what planet is getting the bonus and what that bonus is, it may say something like +8 out of 10. meaning that you're not getttingthe full benefit.

As a note, occasionally you may see that when you move a minber to an asteroid nothing happens, it SHOULD just start mining (you'll see some rings eminating from the miner). IF nothing happens you can click "improve" at the bottom of the screen just to the left of that middle box. i personally avoid using the "automate" order because i don't like my miners trying to move across the galaxy.