Many times when you have a constantly dripping faucet, it can be repaired by simply changing out the valve stem.
A repair man should be able to tell within a couple minutes if it will work or if the valve is too far gone to be repaired.
Even old faucets can sometimes be repaired, some plumbing supply houses stock many older parts or can overnight them to the store.
A tub valve is pretty much the same, but if it can't be repaired, don't be alarmed if it costs between 400-800 dollars for the fixture to be replaced!
Typically, valve stems run from 10-25 dollars per handle and metal or plastic handles are bought separately for a wide range of prices. From 5 or 6 dollars to 15-20 for basic ones and much more for specialty ones.
A repair man or plumber will typically charge a servce call fee for just replacing stems.
The stem in the picture was being replaced this week in a 25 year old home and the part is available at the local hardware store
