First of all find out where you turn the water off. There is usually a valve under the sink, if you cannot locate the valve, find out where the stopcock is this is usually where the mains supply comes into your building.
Turn the tap on and drain any residual water away.
Then locate the screw that removes the head of the tap (the bit you turn) this may be located under a decorative plate.
On modern taps you will be able to get to the washer which will be attached to a spindle that goes into the tap body.
On older style taps you will first need to remove the outer casing or body of the tap using the correct size spanner, once this is off you remove the spindle and get to the washer.
The washer is a small round piece of rubber with a whole in the middle - take this to a hardware or DIY store and get a new one.
Fitting is the reverse of removing it.
Ensure that you tighten but not over tighten the nuts before turning the water on.