Close off the water supply to the tap and open the tap to drain excess water.
Put the plug in the waste outlet - not to stop loss of water, but to safeguard against losing any of the tap components when dismantling it. Remove the top cover of the tap. This may be a metal type with a hexagonal base, in which case you should wrap some cloth around it before undoing with a spanner. The cloth will prevent it being scratched. Hold the tap itself to prevent it turning.
Some taps have a moulded plastic cover held in place with a small screw located in its top (sometimes under a plastic insert, which will need to be gently prised out with a thin bladed screwdriver).
Undoing the tap
Once the cover is removed, undo the top section of the tap by turning the hexagonal nut next to the base with a spanner.
Hold the tap itself (wrapped in a rag) using a pipe wrench to prevent it turning.
Lift the top section out of the tap.
Replacing the washer
On the underside of this will be the washer retained by a small nut, which should be undone, or a button.
Remove the old washer and replace with a new one. Make sure that pieces of the old washer are not left in the seat of the tap before finally reassembling it and switching the water back on.