First, turn off both of the valves that supply water to the faucet. Sometimes these valves have gotten corroded and worn and will not shut off. In that case turn off the main water valve. It's probably attached to the outside of the front of the house. If you can't find it you'll have to shut off the main water valve near the street. Replace the valves supplying the faucet if they don't work.

Start by removing the "H"(hot) or "C"(cold) cover plate. Use something thin like the edge of a knife. Unscrew the handle and remove it. Remove the "stem" with a wrench. On the bottom of the stem you'll see a screw holding in a rubber or fiber washer. Remove it and replace with an identical washer. Re-assemble in the reverse order.

If you still have a leak the "seat" is probably nicked or corroded. You can use a "seat dresser" to smooth it back down. Chances are that once the seat becomes worn your faucet will begin to leak again. You're probably better off with a new faucet.

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