Your valve is not shutting off good, are there is dirt in it. Take it apart and put in new parts. go to http://www.plumbingpartsdepot.com and they usualy show a drawing of the faucet.
what kind of faucet is it, how old is it, is there access to the back side of the faucet area? It might be wise to replace the entire valve. I am not saying that your faucet can not be fixed, it just might be wise to replace it….