Go to a astroid/ice/debree field anywhere. You will see little pieces of roch/ice/debree flying by and when your reticle points at it it turns white and you can shoot it.
Not all of those pieces give loot though and it takes some time and nerves because the areas are usually hide-outs for pirates.

A decent spot to start your mining career off is just south of Pueblo Base in Colorado where you can get silver. Silver sells in Manhatton for a pretty good price so its not far to sell your haul. The Navy and Bounty Hunters from Pueblo will give you plenty of cover, plus there are always other traders and escorts going by who will join in the fray. All you have to worry about is the odd Xeno every now and again. Usually they come in pairs, sometimes alone and occasionally in wings of four. In a Rhino with a decent weapon package you can easily handle one Xeno and usually two. All you need to do in a pair is kill one on its way in and the Navy will nail the other 90% of the time with no help from you (and keep it too busy to bother you much). If they come in fours, just run for Pueblo and park next to it... most of the time the Xeno's don't live long enough to get to you, and if they do you can always dock before they arrive. Not a bad setup for your first attempt at mining. Oh, and as a bonus, killing all those Xenos will slowly put you on the good side of just about everybody.

Now Diamond mining in Omega 11 is a whole other story...

Padriag

One way to mine with our a lot of groups trying to kill you is pay a bribe early as soon as you can afford it to get in good with the rogues. There is a junkers base in Texas where you can do that.

After that almost everyone is neutral. Except the Xenos but this allows you to trade and go outside Liberty and mine.

Be carefull not to spoil this topic. The question is answered so you can leave it alone.

Go to an asteroid field or what ever, and shot those flying things, such as stones, barrels and in California Ice Cloud, the cristmas tree stars, flying towards you. Got it?

The Dom Kavash

the question is already answered, but not all areas are able to be mined,
if you want to know wether a place is minable or not, check "minable zones" in your nav map. : )

adrian M. *u*