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Lift the handle and look for a small hole underneath it, near the faucet's stem. Use the Allen wrench to turn the screw counterclockwise until you can lift the handle off of the faucet. Grip the top of the metal cap with a spanner tool. Turn the cap clockwise to tighten the white, plastic ring inside of it. If your leak was at the handle's base, this may be enough to repair it. Replace the handle and turn on the water to test it. A spanner tool is typically included in the repair kits available for this type of faucet. Otherwise, visit a home improvement store. Using a pair of slip-joint pliers, grip the top end of the metal cap. Rotate it counterclockwise to loosen it. Set aside the cap, then remove the 2 plastic rings inside the faucet to expose the ball. Pick up the ball and look it over to make sure it isn't worn or cracked. If it is, replace it with a new ball purchased from a hardware store or taken from a repair kit. Put the head of screwdriver through the rings and springs to help lift them out of the faucet. Place the new springs in the holes in the faucet, then drop new rubber seats on top of them. Press them down with your finger to set them in place. Place the metal ball on the rubber pieces, matching the ball's groove to the one in the faucet. Put the 2 plastic rings back in place next. Then put the metal cap back in place and tighten it with pliers. Finally, screw the handle back onto the faucet with the Allen wrench.

Summary:
Use an Allen wrench to remove the handle. Tighten the adjusting ring to fix leaks in the handle's base. Remove the cap by turning it counterclockwise. Take out the metal ball and replace it if it's damaged. Replace the rubber rings and springs under the ball. Reassemble the faucet.