Amumu is one of the stronges and best tanks in the game. He gives crowd control, damage and can stand for a long time in a team fight.

Start at blue buff, make sure your team protect you. Make sure you hit all enemies with despair, use a healing potion as fast as u can. then go wolf camp ( Use tantrum when ever it's ready). Then go wraith camp. Then take Red buff and at the end golem. If you can see a gank opportunity go for it, if not go buy and start gank.
*video will come sone*