How do I stop a leaking tub faucet?
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:


a plumbing valve wrench -- I have a set like this:





Teflon plumber's tape.
possibly some replacement washers (but you won't know until you've removed the valve stem).
possibly even a replacement valve stem.


Searching for some information, I came across this article that describes the repair process very well.