I will detail here each step necessary to land your ship safely. Note first of all that this guide comes during Alpha 2.3.1, and that if the development team were to change this game mechanic, a new guide would emerge.
Landing your ship consists of two phases: Decision and Maneuver. Each phase uses an element of your interface: the decision phase is done with your Heads Up Display (HUD) while the maneuver phase is done with your radar. (See image below)
Decision Phase
If you suspect that there is a landing pad not far from your position, switch the controls of your ship to Landing Mode using the "N" key on your keyboard.
All the surrounding landing pads appear on your HUD under these icons:
This icon indicates the distant points of your position, you must approach them before starting anything.
Once you are close enough, the available platforms will be indicated by this icon:
It indicates that the platforms are free and not far from your position.
The targeted platform (closest by default) is indicated by this icon:
It indicates your intention and that you are out of reach to request authorization. To target another platform, use your sight and press the "G" key.
Once you have chosen your platform is that you are close enough, the icon looks like this:
It indicates that you are close enough to the platform to request permission to land.
To request permission to land, press the mouse wheel. The icon then takes this form:
It indicates that access is granted to you and that you can begin maneuvers. The on-board computer will also confirm the authorization by voice ("Access Granted").
Maneuver Phase:
Your decision phase has now come to an end and the maneuver phase begins. The indications are no longer given by the HUD but by your radar and a proximity beep.
Your radar now looks like this:
The red arrows indicate the direction to follow for your approach.
Once you've reached the landing pad, your radar will tell you:
At this point your ship stops and your controls go into maneuver mode. Your ship behaves as if it is in decoupled mode.
Once in the center of the landing air, you need to line up the ship with the platform:
The red areas indicate the direction in which your ship is tilting too far to land.
When your ship is in the center and properly aligned, your radar should look like this:
The white line under the ship indicates the remaining distance to travel. All you have to do is slide down (Strafe Down) slowly to contact with the "F" key. The landing gear comes out on its own when the platform is close enough.
You have landed! 
A confirmation sound followed by voice validation from the on-board computer tells you that you have successfully landed.
To take off
When you take control of your ship, switch to Landing Mode using the "N" key on your keyboard if you haven't already. Request take-off clearance by pressing the mouse wheel. If you are cleared to take off, your ship will rise on its own a few feet from the landing air.
Important Note:
You must not neglect any step at the risk of being penalized. If you land without permission, it is an offense. Stations equipped with defense cannons (No station is equipped with them in Alpha 2.3.1) will not hesitate to fire on your ship! Likewise, occupied platforms do not appear on your ATH. If you try to land on an occupied platform and crash into another ship, you will become a level 1 criminal.
