The drain plug in the bottom of your bathroom sink can trap the water in the sink. This is handy for when you want to wash your face or have some delicate clothes you need to wash by hand. The sink plug is operated by a drain lever on the faucet. Pulling the lever up lowers the plug and traps water, while pushing in on the lever does the opposite. If you're installing new plumbing in your sink, you'll first have to remove the bathroom sink drain plug.
Turn off the water supply. This is usually located on the wall beneath the sink. Rotate the knob clockwise to shut off the water. This will help prevent leaks if someone accidentally turns on the water while you are working.
Press the drain plug lever to the lowest position. The plug lever is usually on the faucet. When properly depressed, the drain will raise to the open position.
Position yourself beneath the sink. Look for the drain plug coupling on the straight piece of plumbing (called the "tailpiece") connected to the underside of the drain. You will see the straight rod for the drain lever mechanism running into the coupling. Unscrew the coupling with your hands, or use a pair of pliers if the coupling is stubborn.
Reach up into the sink and grab the drain plug. If this is a large sink, have an assistant grab the plug for you.
Remove the coupling from the tailpiece by pulling it outward. You will see the ball joint for the drain plug just inside the tailpiece. Pull this out, too.
Pull up on the drain plug to remove it from the bathroom sink.
If the sink is backed up, drain the water before removing the bathroom sink drain plug. Place a bucket underneath the curved section of pipe (the "P-trap") at the bottom. Unscrew the couplings with a pair of pliers and pull off the trap, draining it in the bucket as you do so.