A kitchen copper faucet that's dripping may be a sign of a broken valve or a leaky spout. If the drip is at the base, the parts inside the body have been damaged. To fix this problem, replace the valve and repair the broken seal. To replace the parts, follow the manufacturer's instructions. Turn off the water supply at the shutoff valves and then turn the faucet handle to the "on" position. This will release any pressure and water in the line. Protect the sink by closing the drain and placing a towel in the sink.