It is quite common that a car speedo cable goes dodgy with the time.

The symptoms:

• The speedo needle jumps eratically
• The needle doesn't move at all
• A squeaking noise is coming out of the speedo assembly
  
  Hopefully the process of replacing your Volkswagen Vanagon/Transporter/Typ2/T3/T2 (you name it...) is quite straightforward and easy compared for example to the Peugeot 205 GTI where it can be a pain.
  
  

My VW Transporter T3 is a 2WD, Left Hand Driving from 1988.
Other models may differ slightly from the below pictures.

1. Jack up the front of your VW T3 to remove the front left wheel
2. Unclip and remove the speedo cable square end from the front left hub
3. Remove the front upper grill
4. Remove the instrument assembly to unclip the cable from the back of your speedometer
5. Unscrew the speedo cable mount under the car and swap the cable
6. Put everything back in the reverse order

So here is the How-To replace your VW Vanagon Speedo Cable:

1. Jack up the front of your VW T3 to remove the front left wheel.
That is the square end of the speedo cable you can see coming out of the center of the hub.
Note the white sealing stuff protecting the cable from moisture, dust, etc.

2. Unclip and remove the speedo cable square end from the front left hub.
Remove the white sealing glue (try doing it cleaner that the previous owner...) and remove the C-clip.
The speedo cable square end can now be removed from the hub assembly.

3. Remove the front upper grill.
Unscrew the 5 screws that maintain the front upper grille (yellow dots).
Remove the front grille.

4. Remove the instrument assembly to unclip the cable from the back of your speedometer.
Press/pull the two notches and carefully remove the cover entirely (be gentle with the clips in the front of the cover).

Remove the four screws maintaining the instrument assembly:

You can now unplug the speedo cable by pressing it with two fingers (you can see how mine was broken):

Unplug the connector at the bottom-right (be careful, you don't want to break anything here).
Unplug the cables from the different signal/lights buttons.

You can now remove the instrument cluster completely:

5. Unscrew the speedo cable mount under the car and swap the cable.

The cable goes through a grommet:

You can now swap the speedometer cable: