Hi, I'm Jere_OW, my Summoner is OnlyAmumuSmile because I'm a filthy Amumu onetrick. I don't play much ranked and I know 100% that you shouldn't do this in ranked. This is also my first guide so it's gonna be bad.

When I play Chad Amumu, I usually do this clear.

Blue > Gromp (Smite it) > Wolves > Red > Chickens > Krugs(smite it) > Scuttle > Gank

When doing Red, be sure to use This trick. You can use Despair to agro the chickens, then Bandage Toss to Red buff, then Tantrum the chickens and the buff.

Early game, when you gank, your main goal is to get Dark Harvest stacks, as long as you don't die and you put pressure on the enemy laners, I would say that you are doing a good job. If you have a chance to kill without dying, I'd go for the kill.
If you have maybe a kill or 2, I'd buy a Dark Seal and try ganking more often to scale faster.

Once you get your Stalker's Blade - Runic Echoes, you become terrifying and do big boy damage. You're Bandage Toss is your main source of damage and eventually, your Bandage Toss should reduce your enemy's health to a point where you can proc Dark Harvest, then use Tantrum and some auto attacks for the kill. When you're fighting someone, be sure to keep your Despair activated to deal extra damage and apply Cursed Touch. Your Curse of the Sad Mummy should also deal a lot of damage and will be VERY useful for teamfights.

That's all, I will try to improve this guide once I have more time and a better understanding of how everything works.