Amumu, a sad mummy that is one of the most lethal team fighters when built correctly. In the course of this guide I will be explaining in detail what to do and when to do it.
Jungling upon spawning
The Jungle is a very big and has many monsters that can become difficult if not supported correctly. For example, the Blue Buff(Amumu's best friend) is where you should initiate the game. More than likely, someone will assist you on you getting your buff, but in the rare event no one does here is a tip to overcome it. When beginning the fight on the Ancient Golem you want to stand right in the middle of him and the minions. As he spawns at 2 min mark you should then use Tantrum and activate 1 healing potion. After activating you healing potion smite the golem and continue to use Tantrum until he has died. Once defeated you should then proceed to the Giant wolf. Before fighting the Giant wolf if you soloed the Golem you would have advanced to level 2 which you would then have Despair you will use another healing potion and then use tantrum and activate despair upon advancing to level 2. Once you have defeated the Wolf pack you should then advance into the opposite friendly side of the jungle(the side where you team and turrets are defending) to approach the Wraith. At this point you should have your buff on still and you will be regenerating mana rapidly, therefor you can leave your Despair active. Once at the Wraith you should then activate another potion and move to the center of the 4 birds and use tantrum repeatedly. At this point your smite should be nearly active. You should then move to the 2 Golems and use another healing potion. Once at the golems begin to use tantrum and initiate the fight with them. As you have defeated them and have 1 healing potion left you will move the Giant lizard. Activate you healing potion and move in for the attack. Using tantrum actively will reduce the damage taken so you can survive the last fight before recall. At this point your smite will be active use your smite and destroy the lizard and recall to begin your gear set.
Things you should be cautious of.
Blue Buff Gank: In the beginning of the game people will know you are jungling by the abilities you have chosen(smite and flash). As you learn about the game there is that certain team that will be pushy (this happens rather often once you start to play more and more). The opposite team will creep to your blue buff and gank you at the Ancient Golem. As you will find out there are bushes on both sides of the map in the jungle and both golems on the NE and SW sides have 1 patch of bushes each directly next to the Buff. This makes it very easy to gank if you not expecting it.
Another Jungler: If in the event the opposite team has a jungler as well, you should yield to that and stay alert because he may try to come to your side of the jungle to surprise attack you or even steal your gold/exp. In the event that this happens either call out for a gank upon his arrival or simply take him out upon him stealing your minions/monsters.
The common lane ganks: From the 3 lanes you have mid, top, and bot. You will occasionally have the one or two people that will continuously gank another lane. In the event that this happens, move out into the lane and fight with your teammate if you are not strong enough to take out the ganker alone. Also, you can simply avoid the gank and call/signal it and continue onto what you were doing.
Amumu a pro ganker. Amumu is a amazing initiator. With the ability to flash into the middle of a team fight to cast his ultimate ability Curse of the Sad Mummy He then binds all enemies within a certain area and gives your team a chance to either escape or slay fleeing enemies. Also, in event the curse isn't long enough to get a single champion, you can target 1 person specifically and cast Bandage Toss told bind them for a few more seconds to finish them off or deal additional damage. One of the best initiating moves is cast Despair, Flash into the middle, cast Curse of the Sad Mummy, and finish with Tantrum. This combo is deadly and sometimes so powerful to take out most of the teams hp in just the 2 blows.