Underground drain pipes are used to move water out of the house and send it to the sewer system set up by your municipality or septic system. If you have a water leak in a drain pipe, you will be able to tell by the wet area that will develop in your yard. Repair this as soon as possible, so that the dirty drain water doesn't contaminate your lawn.
Dig out the dirt around the pipe. Shovel off the top grass, and set it aside so that your can replace it later. Dig a long hole running the length of the pipe, so that the pipe is able to bend somewhat.
Cut off the leaking section of pipe, using a pipe cutter. Since this is a drain pipe, water isn't flowing through it constantly. Have someone inside the house run a small amount of water, so that you can find the part of the pipe that needs to be cut. Cut out 3 or 4 inches on either side of the damaged pipe. It might also be a good idea to shut off the main water valve in the house after you locate the leak. This will keep others from running water after you have cut the pipe.
Cut a new section of pipe about 1/8 inch shorter than the section you removed, using the pipe cutter.
Slip the compression nut and the ring onto the ends of the new section of pipe. Slip the compression seat onto the existing piping. Slide the pipe in place, where the old pipe was cut away and into the compression seats.
Slip the compression nut and ring down to meet the seat and screw the fittings in place so that they tighten down onto the pipe and create a seal.
Test the fix by turning the water back on and having someone run water into a sink. Fill the hole back in when you are done, and place the grass back on top.
Before digging, contact the utility companies to come to your house and mark various wires, phone lines and pipes. This will narrow down where to dig by locating the pipe, and keep you from cutting through other important lines.