Amumu starts off kind of slow and boring, and early game people will give you **** for not going jungle, just tell them to stfu. Just go top unless you have to do a 1v2 (with you being the 1) Bandage Toss brings you to the enemy, but it's still a good poke unless they have ranged auto attacks. You won't be doing too much damage, this is when you're just building tanky. Just don't feed, try to get fed, farm, and just play however you think would be best for you.

Okay, by now, (early mid-game) you should have your boots, Rod of Ages, Rylai's, and maybe part(s) of your Deathcap. You can probably mess guys up, but at this point you may need help, atleast try to get as many assists as possible or kills, yeah, kills work too.

Once you hit the 25:00-30:00 mark, you should be able to dish out a bunch of damage and should be relatively tanky, having boots, Rod of Ages, Rylai's, Deathcap, and parts to a Warmog (or maybe a whole Warmog's by now if you're fed enough.)

If you got this far, it's GG for the enemy.
So yeah, basically just build him like this and late game he WILL NOT DIE no matter how hard the enemy tries! He is especially good for team fights with this build, but still AMAZING in 1v1 or sometimes even 1v2, he will deal INSANE damage with his bandage toss and his crying AoE.

Thanks for checking out my guide everyone, let me know if you like or not in the comments, try not to be too harsh/negative, just tell me what I should change (for runes and masteries only, this build's stayin' just how it is :p)