Well, this is my 2nd guide (my 1st being Amumu also, but in lane)
So, beginner's guide to jungling!
If I get better at other champions, I'll also make this guide include them if possible.

21/4/11 - Published guide
20/4/11 - Drafted guide

~Pros~
Great anti-tank skill
Awesome ulti if used well
Easy to get above 10 assists
Syncronize with others well

~Cons~
Skillshot may need practice
Cooldown really long
Easy to kill for a tanker
Small range for ulti
Dependant on skills

mark of vitalityMark of vitality can help with tanking, giving a boost to hp, which is appreciated in most tankers. You can swap this for Mark of Resillence if you want, but not really needed that much.
seal of vigorSeal of Vigor helps you stay in lane in early - mid game and helps alot if you are rushing towers after an Ace. By the time the opponent spawns, you get a nice boost to your hp
glyph of replenishmentGlyph of Replenishment helps in mana regen, important as Amumu doesn't have much mp regen in the 1st place. However, you may want a Glyph of Celerity or Glyph of Focus if you don't get cooldown items.
quintesence of regenerationQuintesence of Regeneration also helps in regenerating lost hp, but can be swapped with Quintesence of Vitality if you prefer to be safer in teamfights.

Ok so basically, 1 21 8 isn't all that good. Basically you follow a traditional non-dodge tank style mastery with some ultility to help.

Some things to note
Try keep your masteries to ? 21 ?, seeing that its good for a tanker. Plentiful Bounty is optional but good for relatively new players. At lvl 30, aim to get either utility buff increase or plentiful bounty. The EXP increase is also important, but can be negated if Zilean is on your team (passive +8% exp)

Cursed Touch reduces the target's magic resistence by 15/25/35 for 5 seconds. This can be useful to assist/kill opponent. It is Amumu's passive and helps quite abit. It upgrades at level 7 and 13.
Bandage Toss throws a bandage at target location. If it hits an enemy unit, Amumu will pull himself to the enemy, stun them and deal 80(increase by 60 each level + 100% ability power) magic damage. The cooldown is 18 seconds for level 1 and decreases by 2 seconds, cost is 80 mp and increases by 10 each level with a range of 1100. Useful stun skill and possibly escape by targetting Neutral Camps
Despair is a toggle skill that saps the opponent hp by % and additional damage. It starts off as 1.5% and increases 0.3% each time, and the bonus damage starts with 8 and increases by 4 each level. It is an invaluable skill against seriously high hp tankers with thornmail.
Tantrum is a skill that is quickly reusable if hit (reduced by 0.5 seconds) and does 75 damage + 50% of ability power (increases damage by 25 each level). Its passive blocks 2 damage per level from every single hit, a useful skill at early game.
Curse of the Sad Mummy is godly - an AOE stun around yourself. Bandage toss/Flash in and a 2 second stun for any enemy kind enough to enter. Useful for turning team fights around and can be used to kill 1v1 or 1v2.

Bandage Toss is pretty useful, but its cooldown is really annoying. However, adding it at level 1 may give a 1st blood to either the person you lane with or yourself, which is good. However, you can neglect adding it if you aren't laning with someone, or that you decide to play defensively. It can be used to stop opponents from targetting your teammate, save yourself by escaping via enemy creeps, but most important of all, gank and killing your opponent. (Luring your opponent to your tower can always lead to a solo lane 1st blood)

Despair is one thing that makes Amumu shines. This skill can do 2.7% of hp as damage, plus 24 magic damage on an opponent. This really helps against tankers, and since Amumu is also a tanker, you can always target your enemy and easily kill without attacking. (Don't bother attacking if the opponent is low on hp, just walk with him and spam skills on him) In teamfights, this may prove to be an invaluable skill.
Note : When Despair is on, towers will aim you if you get too close to enemy champions near it.

Tantrum doesn't seem comparable to the other skills late game, but at killing creeps, its relatively good. It also blocks some damage, wellcome to any tanks. Also note that Tantrum's cooldown is reduced by 0.5 seconds each time Amumu is hit (Except last second). This skill can be used to harrass and can be spammed to kill waves of creeps.

Curse of the Sad Mummy is the best part of Amumu. He stuns enemies within range, enabling your teammates to quickly kill the champions without fear of damage from opponent. It helps with many others' ulti which require aiming or AOE and pretty much can turn an entire teamfight. Don't hesitate to use if your teammates are low on hp in a teamfight - you may just turn the tide.

Traditionally, you start with a cloth armor and 5 hp pots.
After going back 1st time, you should be about lvl 3. Buy a regrowth pendant and a few more pots.
As soon as you run out of pots again (or find that you have 1175 gold), go back to get aphilosopher's stonephilosopher's stone and a heart of gold to boost your cash.
For Amumu, I suggest Ionian boots of lucidity for cooldown reduction. If you go for a ninja tabi or mercury treads(most others are useless)
If you had gotten any boots besides Ionian boots of lucidity, go immediately for glacial shroud. Upgrade to Frozen Heart late game!
As soon as possible, after getting the basic few cheap items, rush for warmog. Remember to get and/or . Ruby Crystal isn't that useful as compared to the others.
Another important thing is your Force of Nature. Even if there aren't much spellcasters, the 0.35% heal is really useful seeing the high amount of hp amumu can reach. Remember to get negatron cloak as its 1st ingrediant for its magic resist. Shurelya's Reverie is the next up your list. It gives Cooldown reduction as well as the boosts you already have from philosopher's stone. Also, it can speed up your teamates in a teamfight to chase down opponents. Randuin's Omen is an important and good tanker style item. Its active slows an opponent for 2 seconds + 0.5 seconds for every 100 armor and magic resist, making it very, very useful.
Now, with your main, godly items, there is few you might buy. If you didn't buy Ionian boots, it means you are free to spam elixers, while otherwise, you will have to buy a last item. Guardian angel can be really useful when packed with your FoN which regens quite abit.

Also, useful items for Amumu ( Tank only ) Thornmail - Useful against carries 2nd Warmog Armor - If you need more hp, regen and armor Leviathan - 2 stacks per kill, 1 stack per assist, each stack increasing tanking abilities and at max cap (20) reduce damage by 15%. But 1/3 is lost per death. Randuin's is a generally good tank item with cooldown reduction (5%) and a slow on attacking enemies as passive. Its active slows down opponent champions around your champion for 35% in 2 seconds + 0.5 second for every 100 magic resist/armor you have. Good item with some tanking ability and cooldown reduction (15%) as passive, with a speed boost to surrounding team champions when activated.
Frozen heart reduces cooldown by 20% and has 99 armor boost, welcome to any long cooldowns. Amumu's bandage toss and Curse badly needs cooldown reduction, so this may be the best viable option

~ Helpful Boosts ~ Sunfire cape - stacks with despair for additional 40 damagerylai's crystal sceptreRylai's Crystal Sceptre - Your tantrum, if spammed, with this item it slows 15%, same for your ulti. If you bandage toss, its 35%. Free slows with spells work well! (Untested with Despair)spirit vistageSpirit Vistage - Cooldown reduction and heal boost is never unwelcomed (not really useful at later parts of game) Guardian Angel - Rebirth is useful, especially in baiting your opponent to go after you instead of your opponent and provides a possible round 2 fight

Jungling is really good in most games since they allow your team to have 2 others to have 1 lane exp, leveling much faster. Even if you decide to stop jungling, you can always lane and help to gank any champion after getting level 4.

Starting off
Blue team - Go bottom lane (Golems)
Purple team - Go top lane (Golems)
Both - Go to close to middle (Wraiths)
Both - Go to the other side NC camp that isn't blue golems (Wolves)
Both - Go back to original golems (Golems)
Both - Go back, smite a Wraith. Engage and run if you need to (Wraiths)

Buy a regrowth pendant and some more pots

Both - You should be level 3 by now. Either go NC the rest of the Wraiths and the Wolves or go Blue Golem for the blue buff (Blue Golem/Wraiths/Wolves)
Both - Go for the lizards or wait till you get back smite by going to the golems (Red Lizard/Golems)
Both - Keep NCing in the order Golem, Wraith, Lizard to maximize EXP and go back 1 last time if needed. Gank if you want.

After level 7, you won't have any problems NCing anymore! Remember to last hit with smite! Calculate the damage or estimate before you smite! In case of enemy junglers finding you, just save smite to prevent buffs from being stolen!

This would be hard for beginners who usually do not have runes. Therefore, instead of going to the usual jungling suggestions, aka the blue golem(buff) and then the red lizard, this guide is specifically for beginners.
Anyway, start off with Golems. Ask your laning teammate to help with killing but NOT taking the exp from the golems. Maokai would be a really good friend seeing his Sapling Toss can help seriously without leeching exp ( 1-3 saplings can easily help). IMPORTANT Save your smite! Use health pot before/ just after engaging golems!
If you have experience increase, you should have been the 1st level 2! Anyway, seeing you saved smite, go to the Wraiths (middle of map). Smite the Biggest wraith (No buffs here) and engage the other 3 Wraiths. Try save MP by only activating despair.
Go to wolves. There shouldn't be much problems by now. Heal whenever you run out of pots and none are activated so as to heal as much as possible.
Keep going in Golems, Wraiths, Wolves in order until you reach lvl 3+ without any pots. Go back, get a regrowth pendant and either level to level 4 by Wraiths and Wolves or else just go Blue Golem (I have problems with it at level 4, so try level 4 for safety). If you smite the Wraiths, you may not be able to get smite in time to kill the Blue Golem, but you probably can take it on without smite.
Red Lizard is your next target. Trash it and make sure you don't get pwnt by it. If you didn't smite the Blue Golem, you may have problems since you taken a lot more damage and regen slowly.
After this 2, just go in the same order of Golems, Wraiths, Wolves to maximize your exp gain.
After level 7, you won't have any problems!
IMPORTANT Always use a pot before jungling! Especially before you get your regrowth pendant! If you have no pots in use or in inventory, just use heal to get abit more hp to NC longer. You can ignore this if you are trying to reach level 4 before Blue Golems (Meaning you aim the rest of the Wraiths and Wolves 1st). Try to buy less than 4 pots after you get your regrowth - You probably won't use some!

Ganking is gang killing, which can be done any time after level 4 (or level 6 for safety). If you do so, its best to aim mid as mid is probably the easiest to kill. Ask your teammate to let them push without being too suspicious, and before the opponent knows it, he may be killed!

You can always go back to any lane that has lost a allied champion, preferably mid since you won't interfere much with the exp flow others get. This way, you can get roughly equivilant exp until your teammate comes, which is your cue to either gank or jungle again.

Some champions have skills that will still work even after you used your ulti. Katarina's Death Lotus, Nunu's Absolute Zero are such skills that will still work even after you used your ulti on them.

Bandage toss does hit creeps, so long as they're not your team. So, to get more accurate hits, try position team fights further from lanes

I would like to thank myfoot1 for being my annoying yet good friend in all my recent games, helping out with jungling. Thanks also to the following people : froggyfrog and KingBisc for helping me out with my games as a jungler, even though they never seen my best yet.
Thanks to Kryptix for his 1st guide, which compelled me to use Amumu the Sad Mummy which turned out to be my greatest champion yet.

Thanks for viewing my guide. Hope it helps!