@Eagle ear, landing is easy.
First centre what your looking to lad on, EG a planet, freeport etc so that when you hit the r key your told something like "freeport ahead 500"(you'll also hear the scanning sound when something is centred).
Then, get closer, you can do this with the o key to engine boost if its a long way, like over 1000 or so. When your at about 300 you'll be told "Can't jump free port"
At this point, carry on checking distance with the r key and also slow down from 10 to about 5, when you get close you'll be told "entering docking field" if it is a freeport or "entering atmosphere" if it is a planet. At this point, hitting p, instead of activating hyper space jump will land you on the given object, though be sure that your within the docking field atmosphere or you could wind up flying off to another system.
To mine, first use the ask for advice menu to get the position of the nearest asteroid field set in your auto pilot (though of course if you see an asteroid field while your out in space and want to check it out you can do that too).
Then, launch. The auto pilot will tell you if you need to jump to another system. Eventually, the asteroid field will be ahead with the r key just like the freeport.
When you've entered the field you'll sometimes run across asteroids in your forward scanner view, you'll hear a beep sound and something like "asteroid 250", if you see an asteroid, fire your laser with the i key and it'll break into meteors. Note that the meteors and asteroids will move so you'll need to pay attention to when the scanning beeps are moving right or left to keep the object in view.
when you have blasted meteors enough, you'll hear a resource such as gold 50, or cobalt 75, when you hear that then fly towards it (you'll also need to keep adjusting your path with the arrows to keep it centred), and pick it up.
Often asteroids will leave rocks behind, which aren't worth anything, if you see a rock then shoot it.
Also, if you have a radar you'll be told in objects in your general forward view, so if you hear a high pitched beep off to your right, it means there's something ahead and right, and you can turn and scan it, note you toggle the radar with the f5 key. I recommend keeping it off until you need it since it can make the soundscape a bit cluttered, though its handy when asteroid mining.
This is how asteroid mining works, nebula mining and gas giant mining work virtually the same way, accept there you don't need to blast the asteroids and meteors to get the resources, they'll show up on your scanner, but bare in mind methane is like rocks, its utterly worthless so if you see it just blast it.
Also, from what I've gathered gas giants aren't exactly rich in resources, you only occasionally see stuff worth picking up, so usually your better sticking with asteroids or nebulae, or indeed trading resources.
hth.
With our dreaming and singing, Ceaseless and sorrowless we! The glory about us clinging Of the glorious futures we see,
Our souls with high music ringing; O men! It must ever be
That we dwell in our dreaming and singing, A little apart from ye. (Arthur O'Shaughnessy 1873.)