The Mk1 Golf has 2 fuel pumps - the main one under neath the car and a 2nd 'lifter' (or 'in-tank') fuel pump within the actual fuel tank.
When to replace - Possible symptoms of a bad lifter pump
Disconnect the batter. Better safe than sorry.
You'll need to remove the rear seat to access the pump. There are two screws towards the front of the seat, undre plastic covers. Remove these and slide the seat forward, then up.
You'll find a circular, black cover underneath where the seat used to be. There are 3 screws holding it in place. Remove these and remove the cover.
Under the black cover you'll find the top of the fuel pump. It's a bronze disc that also forms a lid to the fuel tank.
There will be 2 rubber fuel lines attached to metal inlet pipes atop the fuel pump cover - one is the outlet fuel line, the other is the return fuel line. These will be held in place with radiator hose clips. Undo these clips and slide the rubber hoses off the inlet pipes. Have paper towel ready to soak up any fuel that may spill from these hoses. Be careful to not loose the pipes or hose clips down the sides of the fuel tank.
Next, remove the power socket. Just squeeze and pull gently.
The the fuel pump cover 'screws' into the top of the tank, creating a seal. You will need to turn in slightly - only about 1/6th a full turn - to loosen it.
It may be stiff and may require a tap with a hammer. Use the plastic handle of a screwdriver as a kind of buffer (do not strike the hammer directly on the pump or tank) and tap the top of the fuel pump in an anti-clockwise direction. Be aware there should be a gasket underneath the cover. Ensure this is in good condition.
Once the top of the pump is lose, slowly start lifting it out. This can be kind of tricky. The fuel pump its self hangs below the copper 'lid', along with the return pipe and fuel gauge sender unit (a ball float on a wire). You'll need to be patient and angle all the components out carefully. Pay extra attention to the small filter or sock on the very end of the pump as on some models this is simply stuck on with friction and can be pulled off if caught.
Have paper towel ready to soak up any fuel that may spill from the pump.
The cylindrical pump itself is attached to the copper cover with another rubber hose and radiator hose clip. Undo the clip and slide the pump from the hose. Then, unclip the power socket to the pump.
Attaching the new pump is virtually the reverse of above.
Reattach the electrical socket and rubber hose firmly to the new pump using the radiator clip. Ensure the filter or sock is attached firmly to the bottom of the pump.
Angle the fuel gauge sender float ball, pump and return hose back into the tank. Again, take your time with this and be careful not to knock the sock/filter off (if you do, it can be retrieved with large kitchen tongs). Some people loop string around the filter to hold it in place and remove it later.
Screw the fuel pump cap in by hand, then a light tap with the hammer (remembering to use the plastic handle of the screw as a buffer).
Reattach the fuel lines and power socket. At this point try starting the car to check if the pump is working and that there are no leaks from the hoses.
If all is well, replace the black, circular cover and the seat.