If when the tap is used water leaks from under the head of the tap or the tap judders then the gland packing or O-ring probably needs replacing.
There is one of two types of spindle found in a tap, the rising spindle (older taps) and the non-rising spindle (newer taps).
O-ring replacement - The first is usually found in newer types of taps, it is the non-rising spindle. Initially disassemble the tap. With this type of spindle the circular clip around the top can be removed with a screwdriver and the spindle should then come out quite easily. The one or two O-rings can then be removed with the aid of a screwdriver if necessary. Replace these O-ring/s with new ones with the same inner-circumference (the outer circumference will be worn). The tap can then be reassembled in the reverse order.
Gland packing replacement - The second type of spindle is the older rising spindle. To remove the head (usually a cross type head) find the fixing screw for the head which is usually located under a plug in the centre of the tap or on the side of the head. Once the top of the tap is removed the gland nut is revealed. Initially, try to tighten the gland nut as this could solve the problem, if however it doe not then it must be removed and the old gland packing must be removed. Once the old packing is clear wind some PTFE tape around the spindle and push it down into the gland cavity. Finally before reassembling the tap, grease the spindle to aid removal next time.
O-ring replacement on mixer taps - The base of the centre spout found on mixer taps usually contains an O-ring which needs to be replaced if water is leaking from the spout. Remove the centre spout, usually secured with a retaining screw at its base. Once removed follow the O-ring replacement guide above.