As many different possible builds for Nunu there already is, I decided to publish my very own guide for people to destroy as. Let me start by saying Nunu is a fairly easy class to master if you're good with positioning. When I first played Nunu, I really enjoyed playing as him. Hopefully, my guide will explain any question or teach you something new about this fun champion.
P.S - Please, ignore any of my awful grammar & is a first guide so, don't be to harsh in comments! :) Thanks!

All these were on within like one week of game play with friends at level 30.This was a first game of the day early in the morning. :) Good way to start the day off.

My rune choice is pretty straight forward, AP/Cooldown Reduc./Magic Pen. I can rightfully say don't get Clarity/Mana runes not worth it. You will be getting Blue Golem Buff as much as possible hopefully, not to mention your passive is every 7 auto attacks/melee hits is a free spell, No cost of mana what so ever. Early AP runes you will be hitting pretty hard at level 1-3.

My masteries tree is pretty straight forward, and I would probably confirm as the BEST way to build for as Nunu. Level 1-6 your mana can get a little low if you're up against two ranged or two really good players who know their game play to a certain expense, but usually you should be pushing them back into their turret. 9/0/21 is defiantly a must. (PLEASE READ) - If you would like to jungle as Nunu please, just change out Cripple with Plentiful Bounty and of course get Smite instead of Exhaust.

One thing I will say about this build is that If you prefer to play more defensively pick up the Banshee's Veil first then the Rod of Age's.

LANE

Tome - Crazy early game damage

Health Pot. - Usually don't use this in the lane but i do, on Golem at early level's to pick up a Buff.

Boots/Mejai's - Once you have obtained 1950gold, go get these items.

Catalyst's - mmmm, free hp/mana on level up's + makes you more bulky?

Rod of Ages - More damage!!!

Another Catalyst??? WTFFFFF? - MMMMMMMM, EVEN MORE HP/MANA!

Banshee's Veil - Not dieing anytime soon to dumb nuke champions.

Void Staff - You stack Magic Resist? Well, I Penetrate it.

Deathcap - **** loads of AP, sure why not? enjoy 900-1000 Ice blasts at level 18.

JUNGLE

Ruby Crystal - Health for the jungle.

Boots - Then just the regular build above.

As for what skills to learn, not gonna lie there isn't a best way to build besides the fact that you don't want every skill at level3 when you can have your most useful ability maxed out as soon as possible. Let start with Ice Blast considering you're in a lane. You're going to get this maxed out always. If you're need Heals you're going to get one Consume. Make sure you're using this on the generally stronger minions, just common senses. Blood Boil, where to even to begin explaining this is an amazing move. Not only if you have the Blue Golem's Buff and for pushing towers with team mates but the movement speed alone. Let me not forget, Nunu's passive, every 7 attacks, its a free ability at the cost of no mana. Even if you have the passive ready for use, You can do another 6 attacks and once you lose it, and do your 7th attack and it will be up again. Last, but most certainly not least, ABSOLUTE ZERO. Absolute Zero what an amazing Ultimate to experiment with. Not only is this Ultimate amazing, it hits for a truck load of damage at level.....yeah, all levels....No matter when this ability is used if your enemy's are dumb enough to stand in this, they're most likely died. This ultimate is amazing and all but of course like most amazing ability's there is more to it than just pressing the button. POSITIONING is key to getting this off sucessfully. If a target is running sway and not to close to the turret, you see all other enemy's on the map, Simply, Blood Boil yourself/teammate, Ice Blast him once caught up, Run over him then past him just a little bit then, ABSOLUTE ZERO. Also, one last note, if you mess up with your Absolute Zero, it's not to big of a deal because you can end your Ultimate at any time just simple move to break it and it will still deal quite a bit of damage, of course letting it fully complete it's cast will maximized your damage output. If somebody is about to get out and you know your cast will not finish. Just end it sooner than intended better than missing and hitting nobody at all.

Flash - Flashing on top of 5 people, when they're low. Welcome to PENTAKILL

Exhaust - Now i first had doubts about this just because you already have a slow in your Absolute Zero and Ice Blast ability but i then realized, Exhaust is pro as hell. Use it. Understand it. Profit.

Smite - In the Jungle the Mighty Jungle the Nunu slays tonight. Yeah, Pick up Consume with Smite. Enjoy owning everything you desire.

Basically, if you have any questions add me in-game. Ravertlol/Karaflexlol.
Also, if you have some spare change laying around the house buy Grungry Nunu skin, It's so amazing and awesome looking. :)

In ranked games, Nunu, I actually prefer playing just because of the fact he can do a lot of damage and at the same time actually be strong enough to tank enemy damage. I will say though please don't play a champion in a ranked game unless you've mastered them to a certain point, it's just plain wrong to feed enemy teams.

PROS

-Bulky
-Spam slows
-Consume heal minions
-Amazing Ultimate Damage
-Blood Boil enemy turrets

CONS

-Ultimate can be broke by a lot of the CC ability's.
-Easy for team mates to kill steal you.
-Need patiences
-Mindful of positioning/environment around you.

LANE

-DO NOT EVER ULTIMATE COUGH COUGH COUGH ABSOLUTE ZERO MINION POOLS UNLESS YOUR NEXUS IS ABOUT TO DIE TO MINIONS.

-Melee them, every 7 attacks Blood Boil. Consume stronger minions level 1-12.

-Blood Boil, Consume, Ice Blast spam minions level 12+ considering you have Blue Golem Buff 85% of the time

JUNGLE

-Start by getting Blue Golem Buff.

-From here you have Blue Golem Buff, do what ever is fastest for you. I usually get Red buff at level 3.

-Steal their Blue Buff once yours has like a 25% duration left. Only if you can do it slyly.

-Red Buff is blah really, I just get it for the damage is does, and the slow is nice because once you hit level 6 you should be ganking enemy's out of the Jungle.

You're going to get either people who steal your kills after an Absolute Zero or people who complain because you Ice Blasted somebody they couldn't catch. Please, Blood Boil your teammates AS MUCH AS POSSIBLE.

Flash + Ice Blast + Absolute Zero = Profit.

Ice Blast + Blue Golem Buff = Profit.

Consume + Minion, in a 1v1 = Different Outcome.