Let's see if I can help!
How do I land?
One step at a time! First things first:
How do I request docking access?
You'll have to select the space station on your left hand menu under "contacts". If you click on its name, you'll get the option to request docking.
I'm not sure what kind of controls you're playing with, you can bring up this menu either by "looking" to your left in the cockpit or by pressing 2 on your keyboard (at least i think that's the default).
How do I land?
Ok, now that you requested docking, you can make your way into the space station. They will have given you a pad number that you can land on. The numbers are displayed pretty obviously above the pads, so you can't really miss it.
Before you land, you'll have to deploy your landing gear. This is either found in the menu to your right under the utmost right tab, but there is also a hotkey which believe was "page down". Best look it up in the options again if you play with a keyboard.
How do I quickly get to another planet in the system?
Supercruise! Select the planet in the navigation panel to your left and (again, by default) hit J. That will take you in and out of supercruise (travelling fast within a system) or hyperdrive (jumping between systems).
How do I hyperjump?
Select the system you'd like to jump to in the navigation panel, align with it, throttle up and hit J to jump. It could be that you are 'mass locked' when you are too close to a station. Just gather some distance and you'll be able to jump.
How do I autopilot?
There's no option for that yet, you'll have to fly manually.
You'll be able to purchase a docking computer though which will land automatically for you.
Hope this helps!