There are four primary types of faucets: compression, ball-type, cartridge and ceramic disk. Your Kohler owner's manual can tell you which type you have. Although each works a bit differently, they all have some type of seal that keeps the water from leaking, as well as a valve. Close the water valves under the sink and prepare to dismantle your faucet.
Every Kohler faucet has a hex keyhole either at the base of the faucet or at the base of the faucet's handle. Use a hex key to loosen and remove the top of the faucet. Then unscrew the nut with a crescent wrench to expose the stem, which is held in place in the seat valve with a seat washer and screw. In many case the washer may be broken down, or the valve seat may be worn. If so, replace the washer with a new one or smooth out the valve seat with a valve-seat dresser. This small tool screws into the valve seat; you can purchase one at any hardware store.
Next, check the seal. This is located on top of the seat washer. Compression faucets have rubber washers for seals. Take a look at yours -- it will be easy to determine whether it has worn out. If so, simply replace it. The other three types either have an O-ring or a disc-shaped seal made of neoprene. Again, if they look worn out, replace them and reassemble the faucet.
Kohler faucets have a limited lifetime warranty. If they leak due to normal use, the company will ship you a new cartridge or seal at no charge. This is good only for faucets manufactured after 1997, however.