This tub faucet (that is probably 20+ years old) has a pretty steady drip going and I'm not sure where to start to figuring out how to stop it.
(apologies for the grainy photo...just had my the camera on my phone with me)
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There are several possibilities for the cause of the leak -- incorrect valve placement, a worn washer, a worn valve. All of them will require you to remove the valve stem to investigate. You'll need:
Searching for some information, I came across this article that describes the repair process very well.