To repair a Kohler faucet that leaks, replace the worn O-ring. It is possible to repair the O-ring at home, but you need to have a flat-head screwdriver, a 1/8-inch Allen wrench, channel pliers and a Kohler O-ring kit.
To begin the repair process, make sure the hot and cold shut-off valves are off, and remove the top part of the faucet until you can see the bonnet of the faucet, which looks like a dome with the top missing. Grasp the bonnet, and turn it counterclockwise to remove it. If it becomes stuck, this may be due to hard water, and if this is the case, a bit more elbow grease is the remedy. Fully remove the bonnet to expose the valve and mounting nut.
Remove the spout to see the two O-rings and a nylon gasket. Remove these parts, and take note of how the parts sit. Open the Kohler O-ring kit, and ensure that the new parts are the same as the old ones. Lubricate the new rings and faucet body with the lubricant from the kit, and clean off any hard-water deposits from the housing.
Remove the spout barrel over the body of the faucet, and then move the spout from side-to-side so as to not to move the O-rings. Use some lubricant on the bonnet threads, screw it on, and slide the handle onto the shaft. Tighten the handle, replace the plug button, and open up the valves before testing the faucet for leaks.