Locate the dedicated shut-off valve for your outdoor faucet. This is typically found inside your home, in the basement, crawl space, or a utility closet, on the pipe that leads directly to the outdoor faucet. The valve will usually have a small, oval-shaped handle or a lever handle. Turn the handle clockwise until it is fully closed. If you cannot find a dedicated valve, you will need to shut off the main water supply to your entire house. Once the valve is closed, go outside and turn the faucet handle counter-clockwise to the 'on' position. This will allow any trapped water in the pipe and faucet body to drain out completely. This step is critical for preventing a watery mess during the repair.

Begin the disassembly at the handle. Use a Phillips or flathead screwdriver to remove the screw located in the center of the faucet handle. If the screw is rusted, you may need to apply a small amount of penetrating oil and wait a few minutes. Once the screw is out, pull the handle straight off the grooved stem. Sometimes, handles can be stuck due to corrosion; you may need to wiggle it back and forth or gently pry it off from behind. Next, use an adjustable wrench or slip-joint pliers to grip the packing nut, which is the larger nut situated right against the house or faucet body. Turn the packing nut counter-clockwise to loosen and remove it. Be sure to hold the faucet body steady with your other hand or another wrench to prevent twisting the entire pipe.

With the handle and packing nut removed, the entire stem assembly is now free. Grip the threaded end where the handle was attached, you may need pliers for a better grip if it's slippery. Pull the stem straight out of the faucet body. Since this is a frost-free faucet, the stem will be quite long, possibly 4 to 18 inches, depending on the thickness of your wall. Pull slowly and steadily until the entire assembly is clear of the faucet body. This long rod is what connects the outdoor handle to the valve seat washer deep inside the house.

Now you will replace the parts causing the leak using your faucet repair kit. First, focus on the end of the stem that was deep inside the wall. You will see a brass screw holding a black rubber washer in place. Use a screwdriver to remove this screw and pry off the old, likely compressed or cracked, washer with a small flathead screwdriver or a utility knife. Install the new washer from your kit, ensuring it's seated flat, and reinstall the brass screw, tightening it until it is snug. Next, examine the other end of the stem, near where the handle attaches. You will find one or more O-rings or a packing washer. Use a small screwdriver or pick to carefully remove these old seals. Clean the grooves on the stem with a rag. Lightly coat the new O-rings from your repair kit with plumber's grease to help them seal and prevent tearing during installation. Roll the new O-rings into place. If your faucet uses a packing washer instead of O-rings, simply replace it with the new one from the kit.

With all the new seals installed on the stem, it's time for reinstallation. Carefully guide the washer-end of the long stem back into the faucet body. Push it in gently and steadily until it is fully seated. You may need to gently rotate the stem to help it align properly with the inside of the faucet body. Push it all the way in until the threaded portion where the packing nut goes is exposed and in its correct position.

Reassemble the faucet in the reverse order of disassembly. First, thread the packing nut back onto the faucet body by hand. Then, use your adjustable wrench to tighten it, but only until it's snug. Do not overtighten. Next, place the handle back onto the end of the stem, aligning it correctly with the grooves. Insert the handle screw and tighten it with your screwdriver. Close the outdoor faucet by turning the handle clockwise until it stops. Now, go back inside and slowly turn the water shut-off valve back on. Listen for any sounds of running water and check the valve itself for any leaks. Finally, go back outside and inspect the faucet spout and handle area for any drips. If there's a slight weep from around the packing nut, give it a very small (1/8th turn) tightening with the wrench until the weeping stops.