Do The Right Thing.
How to properly repair a divot mark.
Here are the steps recommended by the Golf Course Superintendents Association of America on how to properly repair divot holes on a green.
Step #1: Take your newly purchased PitchFork Golf divot repair tool and insert the prongs into the turf at the edge of the depression. Note: Do NOT insert the prongs into the depression itself, but at the rim of the depression.
Step #2: The next step is to push the edge of the ball mark toward the center, using your ball mark repair tool in a "gentle twisting motion," in the words of the GCSAA.
This is the step where golfers who incorrectly "repair" ball marks usually mess up. Many golfers believe the way to "fix" a ball mark is to insert the tool at an angle, so the prongs are beneath the center of the crater, and then to use the tool as a lever to push the bottom of the ball mark back up even with the surface. Do not do this! Pushing the bottom of the depression upward only tears the roots, and kills the grass.
Step #3: Once you've worked around the rim of the ball mark with your repair tool, pushing the grass toward the center, there's only one thing left to do: Gently tamp down the repaired ball mark with your repair device or putter to smooth the putting surface.