Bat Wings
If it is truly loose skin, exercising won't make that go away.
What it can do is tone the muscles underneath it and hopefully replace some of the former volume that was filled with fat, and replace that with muscle.
The underside of your arm would be tricep excercises.
check out
http://workoutz.com/
They have video demonstrations of many exercises that you can view and even download. Most of the exercises can be done with no equipment or some resistance bands.
Pretty good for working out at home.
Scott