watch the "How to Mine" video someone else mentioned above (I don't have the URL right now). In an hauler with a 4 bin refinery, 14T cargo space and a tiny bit of luck (mostly compensated by the choice of asteroid belt/ring) I can easily make > 100k pure profit after 20-60mn (depending on the luck thing) of relaxation, listening to music.
The basic process is :
* Probe-mine asteroids until you find what you want. In most cases, that would be platinum, palladium, gold or silver although it's always good to check the boards at your port of call for people looking for particular minerals (20K for 2T of easily found indite for example is a very sweet deal, as you can be sure you'll get it in less than 10mn).
* Once you have found the jackpot (mining is really like scratch-lottery), you check the rotation of the asteroid and try to pinpoint the axis around which it revolves (or at least a point that is halfway steady)
* ... and then you mine away, always on the same spot (technically : always on the same polygon) so that all the chunks line up neatly. If you can't get a straight line you might need to dig in 4 or 5 chunk batches to avoid the ore to decay, collect them and then repeat until no chunks are created anymore.
* Once you have your chunks nicely lined up you select the first chunk you digged up, align your ship so that the rest of the ore form a line away from you. All that's needed is to select the next chunk as soon as you scooped one. Very effective, no hassle ...
* fly to your station of choice which hopefully isn't far.
Lately, of course, piracy in ore deposits in anarchy systems has been on the rise, so you always should keep an eye on new ships appearing and be ready to either fight (if you have any weapons with you) or flee. If you don't have any weapons (And possibly no shields) and someone starts scanning you then don't wait for the scan to end to retract your cargo scoop and hardpoints. If your cargo bay is empty (chunk % don't count as cargo!) you CAN wait to see if the pirate will just leave you alone though. From time to time a psychopath will attack you despite (or because) the fact that you don't have anything valuable, but more oftne than not they'll just let you live.
The whole thing could (and hopefully will) be refined, but right now mining can be quite a nice and interesting activity, especially if you like to gamble. It's not without risks,but the financial rewards can be worth it and most of the time it is relaxing.