I would use mobafire, but its let me down pretty badly in that past. I usually get 
cinderhulk and build tank straight tank and try to get some of the tank items that have some kind of mana from there. Am i building him right?
I like to go with 
as opposed to . Ranger's allows me to power farm and still be super healthy when gank opportunities arise. I almost always go with the 
, although I do believe that 
is a valid enchantment as well if you know how to play Amumu as a mage.
After that my build depends on what kind of a team I'm against and how the game is going.
If the team is full AD I build: 
/
- 
-
where the last item is dependent on whether I need more tankiness, more cdr, or some raw damage. Typically it will be down to the following items: 
.
If the team I'm against is more hybrid damage that my build looks more like the following: /
- 
- - - with the final item once again being dependent on what the team actually looks like.
I would avoid building mana unless it's but since you're building cinderhulk it's probably more benificial to get a instead to benefit from Cinderhulk's 25% bonus health amp.
Another way to build Amumu is a heavy AP build with Magus enchantment recommended for more experienced Amumu players that want to snowball an early lead.
Usefull items for both builds can be and as they increase your damage output, tankiness and utility. Amumu's damage is basically fully within the aura's range and Rylai's gives a permaslow with W active.
For guides in general I would recommend the featured guides on solomid.net, make sure the guide is not too outdated though.
Generally what you want is situation.
You generally want if you're doing well and need mana, however if they have very powerful ADC's you might want
is generally the way to go for smite.
When it comes to offensive items you want either a if your team has a lot of magic damage or if they're mostly AD.
A always helps because it gives you health and CC
and 
are good when against bursters, Banshees for Magic damage, Zhonyas for PD
magemumu too strong O:
(just don't miss Q and make sure your mid doesn't mind you monopolizing blue buff)
Build gives you max cdr, decent AP and plenty of m.pen along with defensive stats for when you dive in. my fave personal amumu build for sure ^_^
Usually, I see people go for a build made out of 3 or more AP items, excluding boots.
Though, while his damage is awesome with AP (and I will always run full AP for fun less serious games, especially in U.R.F- No really, you should try that in U.R.F!), I think that his tankiness is really important.
If things go decent or even bad, I'd stick with , and then upgrade to , and then 
upgrade is situational- If their team has a lot of physical damage and/or their AD Champ/s are doing a little too good and are becoming a threat, I'd pick , if it's an enemy team with a lot of CC and/or is heavy-AP and/or they have champs that are becoming a threat and deal a lot of magic damage, this would be the choice .
I'd go only if I'm doing really good (early especially).
Itemization from there depends on situations like the ones mentioned in the boots section. But remember not to be tempted so easily and pick up too many AP items very quickly (even if I list a few AP items in different sections below) and remember that you can still mix items from the different sections.
Are the enemies magic damage-based mostly? Pick a few of these up: 
Do the enemies deal a lot of physical damage? Take these:
Want to simply deal some more damage and wreck your enemies? You'd like these: 
Some more fun items that I wasn't sure where to list (either because I think they're silly or don't belong to any of the 3 sections): 
Try Probuilds.com, I typically have found good advice there. Pros will build different things to fit their situations, though, but it's great for getting a general idea of what kinds of things you want to build.
I would take Ranger's; his Q has much longer range than chilling smite and is more powerful CC anyways, plus Amumu tends to have mana issues, and Rangers really helps him sustain in jungle. I would build cinderhulk pretty much always; sunfire cape was an amazing item on Amumu, and now you get it for free with your jungle item. The only time I'd build Magus is if I'm just having fun and going full AP, though if you're really good with Amumu and know how to survive fights and stuff, it's another possibility.
