Begin by preparing your workspace for safety and efficiency. First, locate the hot and cold water shutoff valves under the sink and turn them clockwise until they are fully closed. Turn the faucet on to release any residual pressure and confirm the water is off. Clear out all items from the cabinet under the sink to give yourself maximum room to work. Lay down an old towel or bucket to catch any water drips or falling debris. Finally, put on your safety glasses. A headlamp is highly recommended over a handheld flashlight as it keeps your hands free and illuminates your direct line of sight.

Given the assumption of corroded metal nuts, applying a penetrating oil is a critical step. From your position under the sink, aim the nozzle of the penetrating oil spray can as best you can towards the threads of the faucet tailpiece, just above the mounting nuts. Apply a liberal amount of oil, attempting to coat the nuts and threads completely. Allow the oil to sit and work its way into the corroded threads for at least 15-20 minutes, or longer for severely seized nuts. This chemical action will do much of the hard work for you, making the nuts significantly easier to break free.

Before positioning the tool, you must configure the basin wrench's jaw for the correct rotational direction. The jaw is spring-loaded and pivots. To loosen a nut (standard counter-clockwise rotation), the open side of the jaw must be facing to your right as you look down the shaft from the handle. When you turn the handle counter-clockwise, this orientation causes the jaw to cam over and grip the nut tighter. To tighten (clockwise), you would flip the jaw 180 degrees so the open side faces left. Since we are removing a faucet, ensure the jaw is set for loosening.

This step requires patience. Lie on your back under the sink, using your headlamp to illuminate the area. Guide the head of the basin wrench up past the water supply lines and drain assembly towards the base of the faucet. Since visibility is limited, you will rely on feel. Use one hand to guide the shaft and the other to feel for the faucet's threaded tailpiece and the mounting nut. Once you locate the nut, carefully maneuver the wrench head so the jaw slips over one of the flat sides of the nut. Let gravity and the spring tension help hold it in place. You may need to jiggle it slightly to get a good seat.

Once you are confident the jaw is seated on the nut, grasp the T-handle at the bottom of the basin wrench with both hands. Apply slow, steady pressure in a counter-clockwise direction. You will feel the jaw tighten and grip the nut. You may need to put significant force to break a corroded nut free. Avoid jerky movements, as this can cause the wrench to slip off. If the nut is extremely tight, you can insert a long, sturdy screwdriver through the hole in the T-handle to create a longer lever, which will multiply your turning force. Once the nut 'breaks' free, the resistance will decrease significantly.

After the initial, difficult turn, the nut should be loose enough to unthread more easily. You can continue using the basin wrench or, if space permits, reach up and finish unscrewing it by hand, which is often faster. Once the nut is completely removed, repeat the process for the second nut if your faucet has one. When the task is complete, gather all your tools. If you were installing a new faucet, you would reverse the process, being careful not to over-tighten the new nuts. Finally, use your towel to wipe up any water or oil. Turn the water supply back on slowly and check thoroughly for any leaks around the new connections.