The handle of the ball-type faucet rests on a dome-shaped body and is attached by a set-screw. Use an Allen wrench to loosen the set-screw enough to lift off the handle (Image 1).
If the faucet is leaking from the base of the spout, use a spanner wrench (included in the ball-faucet repair kit) to tighten the locking collar by turning in a clockwise direction (Image 2). The repair kit for the ball-type contains the parts necessary to stop a leak from either source. (The ball mechanisms are usually sold separately, but these are seldom the source of the leak.)
If the leak stops once the locking collar has been tightened, no further repair is required. Just reattach the handle.
If the leak continues or is coming from the end of the spout, you'll need to disassemble the faucet. First, close the water-shutoff valves under the sink.
Use slip-joint pliers to twist off the domed cap. You may want to wrap the jaws of the pliers to avoid marring the chrome finish.
Lift out the plastic cam and cam washer to expose the rotating ball. Take out the ball and inspect it for signs of wear.
Inside the faucet are two rubber valve seats that form a watertight seal against the rotating ball. Remove the valve seats by snaring them with a screwdriver. Use caution: there's a small spring behind each valve seat.
If the valve seats appear worn, replace them by lining up new springs and seats on the end of a screwdriver and carefully dropping them into place. Use your finger to press them in firmly. New valve seats should stop any leaks coming from the end of the spout.
If the leak originates from the base of the faucet, pull off the spout and inspect the O-rings. If they appear worn, pry them loose with the hooked end of the spanner wrench. Coat the new O-rings with heat-proof plumbers grease, and pop them into place with the spanner wrench.
Reassemble the faucet by putting the parts back in this order: spout, ball, plastic cam and cam washer, and domed cap. Tighten the collar ring with the spanner wrench and replace the handle.
Turn the water on at the shutoff and check for leaks.