This is my first serious build on a character that I give credit to as the one that got me out of ELO hell. This week Nunu has been free, and there are some miserable players that don't have a clue as to what they're doing. I will just be giving my thoughts on about what a Nunu should be doing and building, and why I consider it to be correct.

Pros:
-Insane early game ganks. With Red buff and E, they can't escape without flash.
-Top tier jungler, because of speed and gank potential
-Can slow enemies AND speed himself and the carry up.
-Ultimate has insane base damage and ratio (+%250 of AP)
-Great counter jungler
Cons:
-Ultimate channel can be broken easily by AOEs, and smart players
-Doesn't deal great damage, regardless of your AP

Marks
Simply Magic Pen. Nothing else to consider

Seals
I go for Flat Armor seals, as this allows me to start jungling with boots.

Glyphs
I like to use AP per level just to slightly better Nunu's lackluster lategame. Other substitutes could be Flat Cooldown, and Magic Resist per level.

Quintessences
I just like to be beefy during early game, for aggressive ganking. Flat HP Quints, along with consume allows for early turret dives, if necessary.

[/color]I use standard 1/19/10 jungling masteries, taking all applicable masteries.

The only MUST HAVE item on Nunu would be Banshees veil, the rest is situational.
Rushing Banshees allow to gank somebody with a spammable stun, such as Sion or TF, with no means to stop you.
Early game, I get boots a mobility, and I'm suprised that nobody else gets it. That, combined with your W allows you to move at 477, while your potential gank victim probably only have boots of speed. I suggest Getting merc treads once the ganking phase has ended.

Rod of Ages - Great item, no downside to it. Get it you feel like it
Abyssal Scepter - Self explanitory item.
Sunfire Cape - If you get stuck being the main tank, god forbid, this is the only real option for armor
Rylais Scepter - If you're completely raping face, you can get this after the Core build. The downside is that the slow from rylais isn't great, because slows are not combined additively.
Soul Shroud - If your team needs more support, Soul shroud can be the item to help top off your Xin Zhaos or Renekton CDR, making them an ability machine gun.
Rabadons Deathcap - I would reccomend this is your last item, if you get it at all. Nunu is better off getting items that benefit his team, because he only has 2 spells.
Void Staff - Cheap way to get AP, and do treu damage to squishies.

Not much to explain here. At lvl 3 I get a second point in Q, just so my HP is sure to be topped up early game, so I dont suicide gank.

1) Make your team watch your blue buff, possibly red buff. At time 1:33, walk over to their wraiths, and Q the big one.
2)Auto attack Blue Buff twice, Pop a potion, and then Q. Auto attack until 445 HP, and then Smite. If you stole their Big Wraith, you will level. Get E, spam E and auto attack 1 creep, Q the other.
3)Go to Wolves, Auto atatck the small one twice and E it. When your Q is off cooldown, Eat the big one and auto attack it once. If you want to Keep your HP high, Lose the last wolf aggro and wait for Q cooldown.
4)Eat Big Wraith, spam E on rest.
5)Q Lizard, Then kill with Smite, or a second Q
6)Q, and then kill one golem. If you need it, lose aggro and Q it when cooldown is refreshed.
7)Time to gank, and you should be at full health. Your victim should be somebody that doesn't have a blink like ability, or flash, indicate to your team who to kill. If you get within E range, they're basically dead with any help from your teammates.
Also, If you get Low HP, Q a minion. You can also do this to eat 1 or 2 turret shots to ensure your teammate the kill, but use discretion.
8)If there are no more ganks avaiable, Go kill your wraiths again.
After that, your blue buff should respawn around 7:30, start your route again, ganking whenever possible.

Ganking - Use your E abililty, auto attack if you have red buff, if they have a blink ability or flash, wait for them to use it. If they don't have flash, or used it, get basically beside them, and pop your ult. after that, E again and auto attack, and Turret dive a little if your Q is up and you have an ideal way to use it.

Teamfight - Ideally, you want to be in a situation where the enemies are running towards your teammates, and you can Ultimate from a bush. If that is not the case, try to hit ANYONE with your E. If you catch 1 person, you will start the fight. Now it is the same as a gank, where you want to permanently slow a weak target without flash. Also, once it has started, after the first stuns have been thrown, you can flash-ult ontop of their team, which will do significant damage, and more importantly, seperate their team. After you ult, hopefully you will have somebody isolated, which will make the enemies run back into a losing battle.

This is my basic guide of how to play Nunu correctly. A tanky support