Mark the ABS/PVC pipe at the location where the other type of pipe needs to be attached. Cut through the pipe at the mark using a hacksaw or handsaw.
Use a portable power saw to make a cleaner cut, or even a powered miter saw. Make the cut straight (at 90 degrees to the pipe), and scrape away plastic fragments or burrs using a utility knife.
Wet the end of the pipe, and push a flexible rubber coupling halfway onto the pipe.
Cut the other type of pipe to size, and remove burrs. Wet the end of the pipe and push it into the other end of the rubber coupling.
The coupling will be half on one pipe end, and half on another.
Secure the rubber coupling to the pipes by using a screwdriver to tighten the hose clamps surrounding each end of the coupling.