It should be realised that a tap dripping at the rate of one drip per second wastes approximately 2.5 gallons every 24 hours. If left unattended it can also cause unsightly stains and even wear lines on enamel coatings.
Identify where the actual leak is coming from and if it appears from the spout, it is probably the breakdown of the washer, while if it comes from the spindle, it is probably the packing that needs to be renewed. Where shower/bath mixer taps are involved, there is an extra washer in the section that diverts the water flow and it is probably this that needs replacing.
Having ascertained the cause of the leak, make sure that the water supply to the tap has been isolated.
Carefully prise off the hot or cold symbol to access the retaining screw and remove it. This releases the body of the tap and allows access to the mechanism.
The spindle should then be reasonably easy to remove and the O-rings eased off with a screwdriver. The outer edges of these may have flattened, but new ones will have rounded edges. Remember, it is the inner measurements that must be the same on both old and new. If necessary wind some PTFE or plumbers fibre around the spindle, push it down into the housing, smear silicone grease around the spindle and tighten down the nut. Finally, reassemble the rest of the tap.
Don’t forget, when fitting a new washer, remove the old one and fit the new one with the smooth side facing downwards.