To land without computer 4 parameters must be correct:

1. Your nose must point in the right direction

2. Your ship must be horizontal.

3. Your ship must be located centrally over the landing area.

4. Your ship must be below a certain height.

Then your ship lands

With the landing computer MK1 only 2-3 (here I'm unsure what's right) parameters must be true.

With the landing computer MK2 only a single parameter has to be correct.

The rest is done by the software for you.

Guide with screenshots

Request Permission to Land

Left click on station to select it.
Right Click to bring up context menu
Select "Request dock at"

You must be within a certain range to dock, so if it is unavailable, you may be too far (or maybe unfriendly with the dock owner.)

Navigate to docking area

Using the green indicatiors, follow them to the approximate docking area.

The green lights may not always indicate the optimal path, so be aware of obstacles in your path.

When you get closer, you'll see a faint hologram of your ship superimposed over the ideal docking location and alignment.

Slowly fly towards this location, being mindful of your speed, position and alignment. It may be best to try and fly above the spot, then descend into it.

Find the docking alignment indicator

As you approach, you should see a red triple chevron symbol pointing you towards the docking alignment indicator. If you are pointed the completely wrong direction, you'll see a U-turn symbol.

Try to center it onto your screen.

Use alignment indicator to land

Your initial alignment may be very bad.

First, center your heading reticle on the target in the alignment indicator and rotate so that you're level.

Now, strafe left/right so that the red triangle with a line above it is centered. When you're centered, you'll see two arrow tips light green.

Now, slowly move forward or backwards to bring the red triangle in alignment. You should see more of the diagram light up green if you're perfectly aligned.

Now, just slowly strafe down until you're docked. You may need to make minor adjustments at the landing pad, but you'll soon be landed.