Turn off the water from the main outdoor water supply. This will be located in one of two places in your home. If you own a 2-story home, go to where the pipes lead outside the house to the leaking spigot and trace this pipe back to the first shutoff valve you encounter. If you own a single-story house, the outdoor water shutoff is located near the hot water tank and will be labeled as an outdoor water supply.
Release the remaining water pressure in the lines by opening the spigot. Next, fit the crescent wrench onto the two flat pieces of metal found on either side of the spigot's valve. These are used to remove the spigot from the pipe. Turn the crescent wrench in a counterclockwise motion to free the spigot from the threaded pipe.
Clean any old sealer from the pipe threads, then wrap the new thread sealing tape over the threads of the pipe at least twice.
Thread the replacement spigot onto the pipe, being careful to trap as much of the thread-sealing tape between the spigot and the pipe as possible. Tighten the spigot down with the crescent wrench so that it is tight, with the valve facing up and the water outlet facing down. Close the valve.
Turn on the water to allow it to flow back into the outdoor water supply pipes. Open the spigot valve to release the air pressure within, then close it again when the water flows freely.