Hello, everyone! I am going to provide you with an excellent support Nunu build following from my extensive personal experience with Nunu as a Support.
Please bear with me as I am new to this Site and it is my first professional Guide.
Thanks for all the help this site has offered me, I feel compelled to link to some outstanding guides:
The best guide to make guides, thank you, jhoijhoi
LoL Etiquette - thanks to Chrismead


Without further ado, I present you: A Guide to a support Nunu & Willump!

Nunu is an excellent supporter because of multiple factors I will adress in the following:

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PROS: The best ASPD buffer Good Harrasser Overlooked Debuffer He's a fricking YETI(-rider) Can save carry from Ganks easily Can help at Dragon with [Consume] Doesn't need much gold to be useful

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CONS: You cannot heal No Shield No hard CC No real big DAMAGE

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For Masteries I use 0/21/9 with focus on defensive masteries and, as you will be warding a lot, take the ward buff mastery in utility. With your mana regen runes and your passive you should have no problems later on, especially once you finished your Philosopher's Stone. Both Flash and Heal/ Clairvoyance are supported in the utility tree, so we master them as well.

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Clairvoyance is a good choice as second spell if you have good communication with your team AND your carry already carries Heal. If you are unsure about your skills at predicting where the enemy jungler will be, rather swap it out for something else. That said, it is a MAPHACK! Who would not want that? Also useful if allies are chasing an enemy and he tries to juke in the bushes... Clairvoyance and he's never gonna get away :D Result: Great at higher skill levels

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Heal is the BAIT/save skill in League of Legends. If you and your carry are low under your tower and Heal is up, save it till they dive you. Then Heal, buff your carry with Blood Boil, slow the enemy with Ice Blast and hopefully get away with a double Kill. Never use it to just "Heal up", it is much more effective in Fights you baited your enemies into. Result: Awesome for a support, even moreso Nunu who lacks an innate healing Ability.

Nunu & Willumps passive, Visionary allows you to cast every spell after 7 basic attacks for free.
You will not be attacking constantly as Support Nunu, rather use you basic attacks to soften up creeps for your carry and retreat once your passive is full. Best used with Ice Blast because it is the ability with the highest manacost on Nunu & Willump (except for his ulti...).

Nunus Q is Consume. It is used for Jungle Nunu, but support Nunu does only need this ability as a form of self-sustain. Therefore we only take one point early. If you are harrasing your enemies and do not fear them, leave it till later and focus on your Ice Blast and Blood Boil abilities. In the Guide I put one point a lvl 4, however you should take one point as soon or late as you feel that you need the sustain.

Nunus W is Blood Boil and it is what makes Nunu such a great Support. It provides a sizable Movement speed and Attack speed buff to both Nunu and the person or minion it is cast on. It lasts for 15 with an equally long colldown which means that (with cooldown reduction) you can even have it active on more than one person at once.
It also works on Minions, which is a nice way to take down a turret if you are solo. Buff a caster or siege Minion (whichever live the longest) and hack away. You should always, if possible, cast it on another person as Nunu his buff for free himself everytime you do it. Only when getting back to lane alone, you should cast it on yourself.
Use it on Autoattacking champs though.
In Lane, use it as soon as there is an exchange between your Carry and them. It provides chasing ability, damage increase and ,if things go south, an escape mechanism. Follow it up with Ice Blast. Do not spam Blood Boil though, your carry should be able to lasthit without your help :)
Later in the game, always keep your nearest teammates buffed as the movespeed can make the difference between a failed gank and the live of an ally.

Nunus E is Ice Blast and it surely is one of his most defining abilities.
Note that it not only slows the enemy, but also provides a 25% DEBUFF on their Attack Speed for 4 SECONDS! Which Means your carry will have the advantage of up to 90% Attack speed TOTAL in comparison to their carry.
In Lane, use it often to harrass overextending enemies: use Blood Boil to get close, fire off an Ice Blast and back off again. It is a quite nice combo.
You use it for the damage and the slow on it, and thus level it every other level, before w.
Not much to say about it elsewise, it does nice dmg though.

And finally, the relevation, Nunus ulti, his R: Absolute Zero!
However, it is not that much of a focus on support nunu, though it is nice because it has the same attack speed debuff as Ice Blast and a sizable movespeed debuff to boot.
How you wanna use it in combat: Never think of it as an AOE Damage ulti. Rather it is your AOE Taunt/Debuff/Pushback/Waste-your-cc-on-me/general confusion Ulti! WOW! Thats even better than damage.... oh yeah it does that too... :D
Thus, you never want to initiate a teamfight with your ulti. Buff your carry, harras with ica blast and keep your distance. If a Teamfight breaks out, wait a little, then run in and use Absolute Zero. The enemy team will scatter or try to focus you / interrupt you. Furthermore the movespeed slow will mess up their positioning and the attackspeed slow will help you keep alive your team. Cancel it as soon as it seems that they are running out of it, some damage is still better than none :)


Skill Sequence:

First of all: ALWAYS counterbuild! If you are the Tank, you have to survive their damage output. You should not be, but will be in the focus nontheless.
Second: After 10 minutes, always buy SOMETHING whenever you get back to base. There is nothing more frustrating than to get killed because you wanted to save for your next "big item" and delayed your Null-Magic Mantle!
Below are items that are reccomended against a balanced team, feel free to mix and match after your personal needs:
Need more health because you just could not get away? Ruby Crystal.
Their AP Carry is fed? Mercury Treads or Negatron Cloak.
You have multiple autoattacking champions on your team? Zeke's Herald.
Your Team doesn't buy defensive items (or only health)? Aegis of the Legion

• : If you feel you need more Health to stay alive, or just some manaregen, get one of these bad boys!
  
• Sight Ward: Always ward! You are the support, it is your job. But warding is lukily enough quite easy to do: Most important of all, you need to know when a gank is coming: simply ward the river a little above your tribush to see them exiting the jungle. That is it!
  Later on, ward Dragon and possibly their blue/red (depending on your side) to see if you can steal them / ambush the enemy jungler together with yours. Always ward Baron and Dragon with a Vision Ward. More in the section about Warding.
  
• : Start with a Faerie Carm and build a Philosopher's stone from it as fast as possible (but still after boots). It pays for itself after 27 Minutes and gives you gold for a free ward every 2.5 Minutes. Later on , upgrade it into Shurelya's Battlesong and don't forget the active to initiate or escape.
  
• : Second is Boots: If you are in no danger from CC or AP casters getting fed, take those. Else take Mercury's Treads.
  Ionian Boots of Lucidity synergize well with Nunu & Willumps Abilities which have all relatively long cooldowns. It takes up to 22.5 secs off your ulti cd and can make the difference between life and death. As you deal most of your DMG with your abilities, it means a 15% dmg increase, as well as being able to consume more often.
  
• : Next up is Rod of Ages. Starting with the catalyst the protector it gives you the much needed health and mana, as well as a nice chunk of AP so that your harras hurts more.
  
• Zeke's herald: This synergizes extremely well with your Blood Boil. It gives your carry that extra Oomph as well as some lifesteal. Furthermore it helps you take down towers even faster and charge your passive even more. Last but not least, it provides you with some invaluable cdr. SOLD!
  
• : This is one of the most powerful items in League of Legends. The Aegis of the Legion gives a total of +78 Armor, +99 MR, +40 attack damage and +270 health... But only if your team is near you.(these are the combined values of the item it gives to you and your team.) It means that every member of your team can take about 12% more physical damage and 15% more magical damage, as well as having 8 extra attack damage. This favours your team greatly in teamfights. I usually get one as soon as possible.
  
• : Use it to ward Baron and Dragon. It is called counterwarding :D

Nunu is a fairly straightforward support: you give a champ ATTACK SPEED and MOVEMENT SPEED.

To utilize this, your carry should have the following attributes:

• good base range (about 600 or more)
• preferably high base aspd ( your Blood Boil boosts by percentage
• possibly on-hit procing effects (higher dps with higher aspd)
  
  Now lets see some examples, which carrys are our bestest friends, and which aren't?
  
  Good champions to support as Nunu & Willump:
  
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• Ashe has nice base range, a built-in slow and good initiation, an overall solid choice.
  
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• Kennen has the hightest base aspd in-game , a good range and an on-hit proc effect with his Electrical Surge. A good matchup.(only when Kennen is played ad)
  
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• Kog'Maw scales very well of aspd, used quite often in competitive matches. He deals damage based of enemies maxHP with his Bio-Arcane Barrage, oh and did i mention it gives him 210 range too..? yes.. very nice!
  
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• Caitlyn has the hightest base range in-game, as well as a procing crit on every 7th hit. A very bullying lane.
  
  Champions to aviod, there are better supporters for them
  
• ezrael
• ezrael has too many skillshots and not that good of a range
  
  
  
  If you end up top lane or something in normal games, Nunu & Willump is also an excellent supporter for melee champs. They benefit a whole lot more from your movespeed buff because it gives you the opportunity

That is all for now, please upvote if you like it and post what you don't like so that i can correct it. I always like critique, but please be honest.

Thanks to jhoijhoi for teaching me all I know about making guides. Peace Out

03/15/2012
Added section about who to support, changed items around a bit, changed masteries