Turn off the water-supply line located beneath the sink and faucets. Turn the valves clockwise until they stop.
Remove the main valve nut from the faucet. This nut is situated beneath the handle of the tap, just above the spout. Place a rag or cloth over the nut to prevent scratching. Use an adjustable wrench to loosen the nut. Hold on to the spout as you loosen the nut, so you don't move the entire tap.
Pull the handle of the tap straight up and out of the main body.
Turn the handle upside-down to examine the valve's washer. The washer is located on the very end of the valve, usually held in place by a small screw or nut. Remove the screw or nut. Pull the washer from the valve. Examine the washer for signs of wear or breakage. It's a good idea to change the washer no matter how it looks, since you already have the tap apart and washers are inexpensive.
Replace the washer. Tighten it down with the screw or nut. Place the valve back down into the main body of the tap. Ensure the spout is facing forward. Place the rag back over the main valve nut again. Hold on to the spout with one hand, and tighten the nut with the adjustable wrench using your other hand. If you do not hold the spout, it will twist sideways as you tighten the nut.
Turn the water valve back on. Turn the tap on.