Begin by clearing everything from under the sink. Place a bucket under the P-trap to catch any residual water. Turn off the hot and cold water supply by turning the handles on the shutoff valves clockwise until they stop. Turn the faucet on to release any remaining pressure and confirm the water is off. Use an adjustable wrench to disconnect the supply lines from the shutoff valves. Next, use channel-lock pliers to loosen the slip nuts on the P-trap assembly and remove it. Use a utility knife to carefully cut the caulk seal between the old sink rim and the countertop. From underneath, locate and loosen the mounting clips holding the sink in place, if any. Finally, carefully push up on the sink from below and lift it out of the countertop. Clean any old caulk or putty off the countertop with a putty knife and a cleaning solvent.

It is much easier to install the faucet and drain before setting the sink. Place the new sink upside down on a soft, protected surface like a towel or piece of cardboard. First, install the faucet. If your faucet came with a gasket, place it over the holes on the sink deck. Insert the faucet's tailpieces and mounting studs through the holes. From the underside, slide on any supplied washers and thread on the mounting nuts. Tighten these nuts by hand, then use a basin wrench to snug them up, ensuring the faucet is straight. Next, install the drain. Roll a rope of plumber's putty about 1/4-inch thick and place it under the lip of the drain flange. Insert the drain flange into the drain hole from the top of the sink. From the underside, slide the rubber gasket over the drain threads, followed by the friction washer and the mounting nut. Tighten the mounting nut securely with channel-lock pliers until the putty squeezes out from under the flange. Clean up the excess putty. Finally, attach the pop-up drain lift rod mechanism according to the faucet manufacturer's instructions.

Test-fit the sink assembly in the countertop opening to ensure it sits flat and level. Remove the sink. Apply a continuous 1/4-inch bead of 100% silicone caulk to the underside of the sink's rim, where it will contact the countertop. Carefully lower the sink into the opening, pressing down firmly and evenly to create a good seal. From underneath the sink, install any supplied mounting clips to pull the sink tight against the countertop. Use a damp rag or paper towel to immediately wipe away any excess silicone caulk that squeezed out around the edges. Allow the caulk to cure for the time recommended by the manufacturer, typically several hours.

Now, make the final plumbing connections. First, attach the new flexible water supply lines to the threaded tailpieces on the bottom of the faucet. Hand-tighten these connections, then give them a quarter-turn with an adjustable wrench. Connect the other ends of the supply lines to the corresponding hot and cold shutoff valves. Again, hand-tighten and then give a quarter-turn with the wrench. Next, assemble the P-trap. Connect the tailpiece coming down from the sink drain to the P-trap U-bend, and the trap arm to the drain pipe in the wall. You may need to cut the PVC tailpiece or trap arm to the correct length with a hacksaw or tubing cutter. Ensure all slip nuts have their tapered plastic washers oriented correctly (taper facing the direction of the seal) before tightening. Hand-tighten all the P-trap slip nuts; they do not need a wrench.

With all connections made, it's time to test your work. Place a dry paper towel under all new connections (supply lines, drain assembly, P-trap) to make it easy to spot small drips. Remove the aerator from the faucet spout to prevent any debris from clogging it. Slowly turn on the hot and cold water shutoff valves all the way. Check for any leaks at the valves and at the faucet connections. Turn on the faucet and let both hot and cold water run for a minute to flush the lines. While the water is running, check the faucet base and all drain connections for leaks. Fill the sink basin completely and then release the water to put a large volume through the new drain assembly, checking carefully for any leaks. If everything is dry, turn off the faucet and screw the aerator back on. The installation is complete.