Turn the water off to that tap. Some homes have mains drinking water to ALL the cold taps, so turn off the mains coming into the house, otherwise follow the next instructions. If it's the warm tap, turn off the respective gate valve in the hot-press, (the cold water valve will be near the main water tank in the roofspace), and turn on the respective tap to empty what is in the pipes.
Once the water has stopped, remove the hot/cold cap and loosen the screw and remove the tap top. If you cannot see the brass fitment, hold the tap spout steady and twist, anti-clockwise, the body. This will reveal the main brass workings.
Once again hold the spout steady and place the correct size spanner on the nut neat the top of the brass unit, and turn this anti-clockwise.
Once loosened, pull it out and on the bottom you will see the black nylon washer. Pry it off and clean the area then replace with the same size washer by just pressing it on with your fingers. DO NOT USE ANY TOOLS AS THIS MAY DAMAGE THE WASHER AND LEAVE YOU BACK AT SQUARE ONE.
Replace the whole tap assembly in reverse order, turn on the water supply and "hey pressto", NO drip.....
Davy Mac, March 2009
