Mark the copper pipe about 5 inches away from where you want to transition the pipe from copper to ABS.
Cut the copper pipe off on the mark using a hacksaw or pipe cutter. Try to keep the cut as straight as possible.
Loosen the nuts on either end of a compression coupler. Place one end of the coupler around the end of the copper pipe where the first connection is to be made. Hold the coupler in place and tighten the nut around the pipe by hand. The compression of the nut on the pipe will hold the coupler in place.
Place a section of ABS pipe into the other end of the coupler. Tighten the nut around the ABS pipe by hand. The ABS and copper ends are now fitted together.
Decide which type of fitting is needed on the end of the ABS pipe. To continue a straight path, choose an ABS coupler. For 90-degree turns, choose an elbow. For 45-degree turns, choose a 45-degree elbow.
Apply a layer of ABS cement to the inside of the desired type of ABS fitting and press it firmly onto the end of the exposed pipe. Allow the fitting to sit for 5 minutes before moving on to the other end of the pipe you just connected to apply the next type of fitting.
Continue adding fittings until the desired pipe configuration is complete.