Turn off the water supply at the shut-off valve under the sink. For double handled faucets, it's only necessary to turn off the water supply line to the one that's leaking.

Tip: If you're not sure if it's the hot or cold water that's leaking you can turn both off. Or first turn the water supply off to the cold water. If the dripping stops, then you'll know that's where the repair needs to be made. If not, turn off the hot and repair as follows:

Remove the handle by loosening the screw on top of the handle. Sometimes there will be a "button" covering the screw (it may have "H" or "C" on it). Flip it off with your fingernail, a screwdriver or a putty knife. Just be careful not to scratch the handle's finish.