Repairing this sprinkler pipe really is a joe shmoe/homeowner type of job. It is incredibly easy, very difficult to screw up, and results in a line that is just as good (and long lasting) as original.
All you do is dig a hole around the bad spot. You then cut out the bad spot. The length of the cut is any distance longer than the compressed fitting and shorter than the extended fitting. Make sure that the cut ends are reasonably clean and dry and put the fitting on without cement to make sure that it is going to fit fine. Remove the fitting. You then smear primer around the outside of the cut pipe ends and inside of the fitting ends. You are not trying to be pretty (the repair will be underground, after all), just smear it on with the brush included in the can's lidgetting good coverage. Let the primer dry for a minute or so. Next do the same smearage with the PVC cement and replace the fitting on both ends of the pipe, giving it a quarter turn as you do so. Hold the fitting for a minute or so until the cement has dried.
The PVC cement is actually a solvent that causes the two pieces of PVC to be welded together. By maintaining good coverage (by smearing it on with the brush) and good contact (by giving it a twist and holding it in place for a minute), you will fuse the pieces together ensuring a repair that will outlive the rest of the system.
Before you fill the hole, pressurize the system (turn the water on). No leak means that you did it right. If it leaks, then you didn't follow my directions. Cut out the repair and try again.