ball mark

what is the proper way to repair the small divot your ball makes from landing on the green? also, what is this small impression refered as? ive seen people dig it up from all angles and others just one angle. after lifting the impression with a tool (i dont know what the tool is called), should it be stepped on or not? thanks in advance

Its a pitch mark and there is only one way to repair it correctly.
YOu need to pull/push the grass back towards the direction you hit from with your pitch mark repairer (sometimes called a divot tool for some reason)
Do not pry up the grass, only push it horizontally back.

Dont worry about digging in a couple of inches back from the mark, you will only get a little bit of movement each time.

then firm it down with your putter and it will be good as new within a few days.
If you try to pry it up you just bring soil to the surface and you will end up with a dead muck spot.

http://www.carlowgolfclub.com/course/pitch.html