First of all, turn off the water supply to the pipe you will be joining to. If a cutoff valve is not located on the line, use a wrench or plumber's pliers to turn the water off at the meter. Layout the pipe to determine where the joint needs to be made. Mark the pipe you will be joining to at the place where the tee fitting will go with a marker.
Then cut the pipe you will be joining the new pipe to with a twisting tube cutter for copper pipe or a ratcheting cutter for PVC. Cut the end of the pipe you are joining to the original pipe to length. Make the cut smooth to ensure a good fit. Separate the compression nuts and rings. One nut is at each opening---three nuts total.
Thirdly fit one compression nut onto one end of the original pipe, with the threaded side facing the cut end, and slide it up several inches. Slide a compression ring onto the same pipe. It will have two openings straight across from each other, and one at 90 degrees to them. Place the pipe with the nut and ring into one side.
Lastly, push the nut down to the pipe fitting, with the compression ring between the nut and the fitting. Twist the nut onto the fitting by turning clockwise until it is snug. Use plumbers pliers to turn it one and a half turns more. Repeat by inserting the other side of the top of the fitting into the remaining end of the original pipe. In addition, place a nut and compression ring on the end of the intersecting pipe, and insert it into the remaining opening of the tee. Twist the nut tight as before.