What kind of faucet do you have? If it's a common brand it should be just a matter of replacing washers or seals (depending on the brand). If it's a single handle Moen, then you get into a cartridge which might cost $20-$25...almost anything else should be less than $10. Come up with a brand name and whether it's single or two handle.

coolvt - Thanks for the response. Its a Price-Pfister and its a single handle. Thanks again.

If you have a PF and it's about 20 yrs old then in may be a 809 series. If this is the one, there is just a cartridge to replace. I believe the factory part # is 974-272. The picture in my book is showing a trim piece that is rectangular in shape and wider than it is tall.
If this sounds like the model, I would call around to pluming supply houses to find who may have parts. I doubt that it's going to be something that Home Depot carries. If someone carries PF I would bring the part with me.
I think to disassemble it....take the handle off, remove the chrome ring (I think it just slides on) and then you should see an 8 sided collar nut. Remove this nut and you should be able to pull the cartridge out. You may have to put the handle back on the stem sticking out of the cartridge to have something to pull on.
Hope this helps.
Mark

coolvt - Thanks for your helpful e-mail. I called PP and the cartridge assembly (?) is on back order (of course!). I reinstalled the old one and will keep my fingers crossed until it arrives in the mail. Thanks again.