My initial response for anything related to skill shots is "practice makes perfect". However, here are some additional tips I have picked up (since Amumu was a favorite of mine for awhile):
* Timing: understand how long the animation takes and what the range is.
* Know thine enemy: predict where your enemy is going or where he will be. When I first started using the bandage toss, I primarily used it when an enemy was going straight towards me or straight away from me (this helped me to get a firm understanding of bullet #1). However, I really started to excel when I saw an enemy turning a corner and I guesstimated what angle to shoot.
* Bandage goes through walls, trees, obstacles, etc.! Yes, you can get many surprise attacks on people by jumping out of the woods, following Anivia through his ice wall, or even jump through the walls of the enemy base.