Wipe the dome with a warm, damp washcloth to eliminate dirt that could be impeding function. This also makes it easier to find cracks and other damage in the sprinkler head.
Place a check valve underneath the dome sprinkler if water leaks from the opening when the sprinkler isn't on. This is often a problem when the sprinkler is near the bottom of an incline because the pressure created by gravity forces water through the sprinkler head. Pull the dome off of the sprinkler, screw the check valve onto the riser and then push the dome back into position over it. You might need to dig up the valve with a shovel if you can't reach it manually.
Inspect the dome to look for cracks or chips in the housing.
Apply an epoxy to any cracks or breaks in the dome to reseal them and to repair the damage. Allow the epoxy at least an hour or two to dry before using the sprinkler again.
If water flow is a problem, verify that the water valve leading to the sprinkler head is open. A closed valve won't allow the sprinkler head to function until it is opened.