It is very irritating to listen to a shower drip, drip, drip. A worn out faucet usually causes this drip. There are several things that may need to be replaced. The rubber gasket may be worn and not sealing correctly. The faucet handle may not be turning completely off. The shower may need a new cartridge. If your not sure exactly what the problem is, and have little plumbing experience, you would be better off to just buy a complete faucet set and replace the entire faucet.