If a tap drips from the spout even when turned off tightly, it's likely that the washer needs replacing. Most taps are similar and replacing the washer is not difficult. You'll need to buy a new washer of the correct size from your local hardware store. If you know what the size is, you can get the new washer prior to step one. Otherwise, after step three, take the old washer with you to the hardware store to match the the size of the new one with it.
Turn off the water supply feeding the tap.
Use an adjustable spanner to unscrew the tap cover, inserting a soft cloth between the tap and the spanner to avoid scratching the metallic surface.
Unscrew the large gland nut inside with an open-ended spanner and lift out the old washer.
Replace it with the new one.
Reassemble the tap and turn the water supply back on.