Scott Manley made a tutorial for Asteroid Mining. Watch it below. After the video are some advices from other commanders. And if you need more guides and tutorials then visit this page.
And here are few advices from the Elite forum:
I've noticed there are some questions about mining and not many answers, so for those who want to get into that and make some decent credits in a reasonable amount of time, here goes:
When you start, get a hauler (u start with around 80k credits) suit it up with most basic refinery and mining laser (all obtainable at Aulin and Styx) and head out to an asteroid field. best bet is an metallic asteroid field, the only ores worth the hustle is gold, palladium and platinum, don't bother with anything else (at least at the beginning when u have very limited cargo space).
When you mine don't chase the rock chunks (it will make your mining that much time consuming), position yourself about 3/4 of your mining laser range away from the asteroid and when you separate a chunk of ore just use your directional thrusters to position your ship in front of the incoming rock. The veloctiy of the rock will do the rest for you, always try to aim at the middle of the asteroid when you mine so the chunks don't fly in any crazy directions that will give you time to re-position your self to intercept.
I was making about 50k every 15-20 min with my Hauler using the above technique. If anybody has any thing more to add I'd be glad.
BTW mining is pretty cool visually, usually metal asteroids are close to the sun so the view is breathtaking.
If you play around with the laser angle on the asteroid you can redirect the expulsion stream towards your scoop as well.
Listen carefully, I'll shall say this only once. Find Kaurawish. The first and second ring has roids containing Gold and Palladium. Dunno about the other rings, but I have been visiting the first 2 twice with good results.
I cheat a bit . . . I'm mining palladium and indite but only one rock in the cluster has it. Once it's exhausted I exit to main menu and reload game, find right asteroid (easy, it's the smallest of a group of 6) – rinse repeat. It's not that great but just made about 70k in 45 mins.
I would honestly recommend not even approaching mining until you can get yourself 4 bins – it is hard work with less, as you are constantly dumping captured ore when you come across better ore, then your stuck fragging roids till you find higher quantities of that ore.
I got my Cobra set up with 4 bins and headed off to a set of A Rings and magic started happening.