Unfortunately, the parts inside a kitchen sink's tap do not last forever; sooner or later you will have to replace them for the tap to continue functioning properly. Your local plumbing supply centre or hardware store carries replacement parts, as well as plumber's grease, that will allow you to fix your tap. Take the old parts with you to the store for comparison if you are not sure of the brand of your kitchen sink tap; if you don't get the right parts, either they will not fit on the tap at all, or the tap will leak water.
Close the house's main water valve by turning the handle to the "off" position. Turn on a tap, at a lower level if possible, to make sure the water flow in the house has completely stopped.
Remove the tap handle's retaining screw, located either at the bottom of the handle's base or under a cap on the top of the handle's base. Lift the handle off the tap and set it aside.
Back out any retaining screws or adaptor pieces once you have removed the handle, using a Phillips screwdriver and a spanner. Pull out any metal clips or pins that are still present in the tap, using a pair of needle-nose pliers.
Use a spanner to twist the tap's valve cartridge counterclockwise to remove it from the tap. If the tap does not have a cartridge, remove the rubber seats and metal springs, using a pair of tweezers.
Lift and twist the tap's spout to remove it from the tap assembly. Pry the rubber O-rings off the tap's base, using a flathead screwdriver. Coat the new O-rings with plumber's grease, then slide them onto the same positions as the old O-rings.
Slide the tap's spout back into place. Coat either the new cartridge or seats and springs with plumber's grease, then reinstall them and the other pieces you removed from the tap, in reverse order from the way you removed them. Replace the tap's handle and retaining screw, then open the main water valve for the house and turn the tap on.