Every water appliance in the home has its own shut-off valve. When turned off, that appliance stops receiving water without affecting the other water appliances. Each of these valves has two nuts that have the potential to leak, if they are not tight enough. The main nut that holds the valve to the end of the copper supply pipe is the compression nut. The second nut is smaller and connects the water supply hose to the top of the shut-off valve.
Place an adjustable wrench around the body of the shut-off valve. Tighten a second wrench around the compression nut (found on the bottom of the valve, surrounding the copper pipe).
Tighten the compression nut in 1/8 turns, until the leak stops. If the leak continues, tighten the water hose nut.
Place the second wrench around the water hose nut, keeping the other wrench around the valve body. Slowly tighten the water hose nut, until the leak stops. If the leak doesn't stop, replace the valve following the steps below.
Turn off the water at the main shut-off valve. Place one wrench around the valve body. With the second wrench, loosen and remove the water hose nut. Then use the second wrench to loosen the compression nut.
Pull off the shut-off valve by hand. Use pliers to remove the compression ring, and pull off the compression nut by hand.
Slip a new compression nut over the end of the copper pipe--by hand. Push the new compression ring down onto the end of the pipe--one inch from the end. Place the new valve onto the end of the pipe.
Hold the new valve body with one wrench, and with the second wrench tighten the compression nut onto the valve body. Then tighten the water hose nut to the top of the valve with the second wrench.
Turn the water back on. If the valve leaks, tighten both compression nut and water hose nut in 1/8-turns, until the leak stops.
If both nuts have been fully tightened, and the leak continues, the valve will have to be replaced with a new one. The compression ring is a brass ring that looks somewhat like a gold wedding band. It is positioned around the pipe between the valve body and compression nut.
Don't over-tighten either nuts, or the threads may break off. If this happens, the valve will have to be replaced.