Fixing a leaking pipe underneath a sink is a simple DIY job and one that will save you a considerable amount of money as opposed to calling a plumber. If you notice water leaking at the point where two drain pipes connect, then you need to replace the slip nut and its washer. This is the most common cause for drain pipe leakage beneath a sink, since the washer wears away with enough use.
Set the slip nut onto the drainpipe with the threads of the nut facing the threading on the pipe that you want to connect it to.
Push the slip nut washer onto the pipe with the slip nut on it. Make sure the thicker end of the washer is facing the slip nut.
Insert the pipe with the slip nut and washer into the pipe that you wish to connect to.
Press the washer into the gap between the two pipes. The tapered end (thinner end) of the washer should be going into the gap between the two pipes first.
Wrap a piece of plumber's tape on the threads of the pipe without the slip nut on it. PVC pipe does not need plumber's tape.
Screw the slip nut onto the threading of the other pipe you want to connect to. Use a plumber's wrench to tighten the slip nut if your drain is steel or brass.