The majority of new taps installed today have ceramic discs fitted inside as they are quite low maintenance fittings. Just like all things they are prone to failure and will need replacing if they do. If this happens, you can take the job on yourself or call on the services of a professional tradesman like an Archway Plumber who can replace taps and other fittings. There are two ceramic discs that contain two holes in each and when a tap is operated one will move with the handle and the other one will remains static. When the holes in the two pieces align, the water will then flow. If this type of tap has a leak it means that the ceramic discs have suffered some damage and the holes are out of line. The discs themselves are not replaceable so this means a cartridge replacement is needed. If you are not confident to do this task, then call a professional like Archway Plumbers who can fit the cartridge. They are right and left handed respectively so the right orientation must be observed.Clean or Replace:Isolate the water supply to the taps. Turn the taps on separately and drain the water away through the open taps. Remove the heads from the taps. These can be one of two different types, the first a push on fitting or the second that needs a screw to secure it. When this is complete, hold the tap body so that when you undo it, it will not rotate with the turning action. Remove the cartridge. Remember the orientation either left or right mentioned earlier. Once out, visually inspect as it could be just debris inside and may just need clearing. If this is not the case, then, replace the cartridge. Check the seal for damage while you are in there. Fit new if needed. Make good and de-isolate the water supply and check for leaks etc.