The 2nd post! Thought I might go with the N64 controller. This controller is nortorious for getting broken, trashed control sticks. As such its still very easy to buy brand new control sticks which are very simple to replace.
As you can see there is 8 screws on the back. The good news is is that they are No1 Phillips so no fancy bits required. Make sure you use a No1 (Thats a small headed Phillips) and not a No2 (Regular size) as you will strip the screw heads.
Pop the back off and you can see the board. There are 3 screws holding the control stick in. The blue dot there is a 4th screw, leave this in, it just holds the control stick together.
Here is the front of the circuit board, not much to it really. The control stick is attached by 5 wires and a plug.
Here you can see the cable connecting the control stick. The blue part there is for the Z trigger. It just unclips off the control stick. Replacement is as easy as undo that plug (dont pull on the wires, use a tiny flathead screwdriver to pry it loose), and plug the new one in.
If you undo the screw in the control stick and the 2 clips it pops open. There are two small cog elements inside which are connected to transducers to turn the movements into electrical signals. It can get fairly dirty in here due to build up from the plastic rubbing away (thanks to Mario Party).
Anyway, thats it, remember, do it at your own risk, and dont blame me if it goes wrong.