The steps to replacing a dripping shower valve cartridge are pretty straight forward.
Be sure to turn off the water supply to the faucet before you begin.
Remove the handle, usually held on with an allen (hex) wrench.
Remove the valve sleeve
Remove the escutcheon (face plate), this will depend on how far the valve is recessed in the wall. Whether you can get to the retaining clip.
Remove the retaining clip
Pull the cartridge from the valve
Watch the video to see this procedure in action.
Great idea