Mining isn't too developed in Freelancer-

When you go into an area where the map indicates it's minable, look for little rocks that fly around. When your cursor goes over it, it'll change. Shoot it. It'll take a while for you to get anything, and it isn't too profitable.

Hi crest, welcome !
Mining areas deliver a different amount of commodities like diamonds, gold, water and so on. In some asteroid fields you have to shoot at many little flying rocks (as MercZ pointed out) until they give free what's "in" them. Best practice: stand still and use H-key for turret view; otherways drive slowly through the asteroids and shoot at the moving rocks.
In some mining areas you can be successful easily and fill up your cargo hold in short time - and for FREE ! In case of you did not know already: Of course you have to use your tractor beam {B-key} to collect the commodity in space.
But watch out to have a neutral or good reputation with the factions in the area. It can be annoying when you have to kill again and again attacking ships when digging for gold .

The laziest way of mining my son just discovered in Evolution 1.28 (but it might work in unmodded FL too, I haven't tried this):
put your ship very close to an asteroid miner (ship). Wait until this ship "gets" a commodity - then push your B-key very fast for tractoring it in .

Also use your nav map to find out if a system produces anything! Some systems have nothing mineable at all.

Each mineable area will usually have a few spots that are rich in ore. It can take some hunting around to find these.

And early in the game, you can pick up money to buy better equipment simply by salvaging scrap metal in debris fields.