Before beginning any work, locate the hot and cold water shutoff valves, typically found in the cabinet directly beneath the sink. Turn the handles clockwise until they are fully closed. To confirm the water is off, turn the faucet handle to the 'on' position; any remaining water in the line will trickle out, and then the flow should stop completely. Lay a towel in the sink basin to protect the surface and to catch any small parts you might drop. Gather all the tools and supplies you will need for the job to have them within reach.

Examine the faucet handle to find how it is attached. Most single-handle faucets have a small set screw, which is often hidden behind a decorative cap marked with a red/blue hot/cold symbol. Use a small, flat-head screwdriver or a utility knife to gently pry this cap off. Inside, you will see the set screw. Select the correct size Allen wrench from your set and turn the screw counter-clockwise to loosen it. It only needs to be loosened enough to allow the handle to be removed; you do not need to take the screw all the way out. Once loose, lift the handle straight up and off the faucet's valve stem.

With the handle removed, you will see a decorative dome-shaped cap covering the top of the faucet body. This cap is usually threaded on. Try to unscrew it by hand first. If it is too tight, wrap a cloth or rag around the cap to protect its finish, then use a pair of slip-joint pliers to grip it and turn it counter-clockwise. Once the cap is removed, you will expose the faucet's cartridge and the top of the spout assembly. You can now grasp the spout and pull it straight up, wiggling it slightly from side to side if it's snug. This will lift the spout off the main faucet body.

After lifting off the spout, you will see several grooves on the faucet body that hold rubber O-rings. These O-rings create the seal that allows the spout to swivel without leaking. Use a small pick tool or a flat-head screwdriver to carefully dig into and pry the old O-rings out of their grooves. Take the old O-rings with you to the hardware store to ensure you get exact replacements, or use the ones from a faucet-specific repair kit. Before installing the new ones, clean the grooves on the faucet body and the inside of the spout with a cloth, using a small amount of white vinegar to dissolve any hard water deposits. Apply a thin layer of plumber's grease to the new O-rings; this lubricates them, making reassembly easier and protecting them from tearing. Carefully stretch and roll the new O-rings into their designated grooves.

Reassemble the faucet by following your disassembly steps in reverse order. First, slide the spout back down over the newly installed O-rings onto the faucet body. You should feel it seat firmly. Next, place the decorative cap back over the top of the faucet and screw it on. Hand-tighten it firmly, and if necessary, give it a very slight final snug with your cloth-wrapped pliers, but be careful not to overtighten. Finally, place the handle back on top of the valve stem, ensuring it is oriented correctly. Tighten the set screw with your Allen wrench until it is snug, and then push the decorative cap back into place on the handle.

With the faucet fully reassembled, you can now test your repair. Go back to the shutoff valves under the sink and turn them counter-clockwise slowly to restore the water supply. Open them all the way. Check for any immediate, major leaks. If none are present, turn the faucet handle on and let the water run. Swivel the spout from side to side and move the handle to mix hot and cold water. With a dry paper towel or your fingers, carefully check the base of the spout and the area where the faucet meets the sink for any signs of water. If it remains dry after a minute of operation, the leak is fixed.