Determine the material of the existing pipe you are connecting to. New PVC pipes can be connected to metal and PVC of any size with metal or PVC pipe fittings.
Determine if you are connecting to a male or female end of a pipe. Male ends are threaded on the outside and go inside a female end. Female ends are threaded on the inside of the pipe.
Measure the diameters of your existing pipes.
Select the proper fitting at the hardware store based on the diameter of the pipes you are working with.
Connect to a male end of a metal pipe by attaching a metal fitting with two female ends. Clean the threads with a wire brush and apply plumber's putty to the threads. Then screw the fitting onto the existing pipe. Apply PVC cement to your new pipe and insert it into the fitting.
Connect to a female end of a metal pipe with either a PVC fitting or metal fitting that will accommodate the end of the old pipe with a male end and will accommodate your new pipes with the appropriate diameter on the female end. Apply plumber's putty to the threads and screw the connector onto the old pipe.
Connect PVC pipes together by coating the outside of the male end and the inside of the female end with PVC cement, then slide the male end into the female end. Wait for the cement to dry according to the manufacturer's directions.