Things You'll Need
Teflon plumber's tape
The sink tailpiece is the pipe directly below your sink that connects to the drain on one end and to the curved P-trap on the other. If the tailpiece is leaking, then water is falling inside your kitchen or bathroom cabinet. The best way to correct a leak is to replace the pipe, as chances are the part is rusting or cracked and any repairs are likely to be only temporary before new leaks start up. Save money on a plumber by doing this project yourself.
Turn off the faucets and place a bucket below the pipes under the sink to catch any water
Twist the nut on the top end of the tail piece to the left to loosen it from the sink drain, using a wrench. Detach the other end of the tailpiece from the P-trap in the same manner.
Wipe the threading on the sink drain and the P-trap with an old cloth to remove grime.
Wrap Teflon plumber's tape from the tip of the pipe on the sink drain, working upward toward the bottom of the sink. Apply tape only to the threads, and press the tape on all sides. Wrap a separate length of tape on the P-trap threading.
Connect the bottom of the new tailpiece to the P-trap using the nut loosened in Step 2. Tighten the nut to the right by hand, then seal the connection with 1/2 turn using the wrench.
Slide the nut on the sink drain onto the top of the tailpiece and turn to the right to tighten, completing the seal with a 1/2 turn using the wrench.
Turn on the water and let it drain through the sink to check your work. Tighten the top and bottom connections on the tailpiece if you see any leaking water.