You don't need special plumbing skills to remove one piece of a drain pipe on a bathroom sink. The drain pipes for bathroom sinks typically have three different pieces: the tail piece, the P-trap and the drain elbow that connects to the pipe that extends from the drain system inside the wall or floor. To remove the drain elbow or tailpiece, you need to detach the slip nut on the P-trap where it attaches to the pipe you want to remove. Have a bucket handy to catch water stored in the P-trap.
Access the plumbing underneath the sink. If the sink sits in a vanity, open the cupboards and clear out everything underneath the sink. Set the bucket beneath the P-trap to catch the water that comes of it while you work on it.
Set the slip-joint pliers on the large slip nut where it connects it to the drain pipe you need to remove, whether it's the tail piece that extends from the sink or the drain elbow that attaches to the drain in the wall or floor. Loosen the nut by turning it counterclockwise. Move the slip nut back onto the pipe you want to remove.
Move the P-trap out of the way. Make certain the bucket stays beneath the open end of the P-trap to catch any water that spills. You may have to push down slightly on the P-trap when removing the tail pipe because it sits inside the P-trap. Next, turn it to the side. When you want to remove the drain elbow, pull down slightly on the P-trap, then swing it out of the way.
Disconnect the tail pipe. The tail pipe might also have a stopper and control rod attached to it for closing the bathroom sink. Detach the round nut at the back or side of the tail pipe that connects the control rod. Pull the control rod with a round plastic ball on it out of the tail pipe, then lift the stopper out of the sink. Loosen the slip nut on the tail pipe by turning it counterclockwise where it attaches to the drain flange. Slide the slip nut down the tail pipe and set it aside. Remove and replace the tail pipe.
Remove the drain elbow. Disconnect the drain elbow from the drain pipe by turning the nut counterclockwise with the slip-joint pliers.