A dripping tap can easily be fixed through any of the following means:
Change the cartridge or washer depending on the design of the faucet: turn off the water supply and drain the system. Pry off the cover of the faucet and remove the screw. Use an adjustable wrench to loosen the nut counterclockwise. Remove the headgear/cartridge and fit in a new one. Reassemble the tap and turn on the water supply.
Grind the seat to stop drips: if, after you have changed the washer, the faucet still drips from the spout, it may be that the valve seat (the part pushed against by the washer) is worn. You could use a nylon liner to make a new valve seat or grind away a little of the metal to form a new, flat seat.