After turning off the water at the shutoff, locate the set-screw and loosen it with an Allen wrench to remove the handle.
Under the handle is a decorative escutcheon cap that may screw or pop off. With the cap out of the way, remove the cylinder mounting screws and lift out the cylinder.
Remove the neoprene seals and check them for debris, damage or wear. If the disc below the seal is dirty, try cleaning it with an abrasive kitchen pad, then rinse and replace it. If the seals are damaged, replace them. This may be all that's required to fix the problem. Reassemble the faucet and check for leaks.
Important: Before turning on the shutoff valve to check for leaks, first turn the faucet to the on position, then very slowly turn on the water at the shutoff valve so any trapped air escapes gradually. Otherwise a pocket of air might be forced under great pressure into the cylinder and could crack the discs.
If the faucet still leaks after cleaning or replacing the seals, one of the discs is probably damaged. You'll need to repeat steps 1 and 2 in preparation for replacing the cylinder.
After turning the water off and removing the escutcheon cap and mounting screws, carefully lift the old cylinder out of the faucet body and drop in the replacement.
It's often difficult to see damage to ceramic discs inside the cylinder of a disc-type faucet. Placing a drop of food coloring inside the cylinder openings may reveal hairline cracks in the disc that aren't otherwise visible.
Reassemble the faucet: tighten down the mounting screws, replace the escutcheon cap, and reinstall the handle.
Turn the faucet to the on position, and slowly turn on the water supply at the shutoff valve to check for leaks.