When supporting as Nunu, make sure to be a bully in lane by constantly harassing with Ice Blast and making the enemy target you. It is easy to use Consume on cannon minions without taking CS to recover health. If the enemy duo decides to focus you and spend CC, use Blood Boil on your carry and fight. This strategy is effective, but can be mana heavy, so be sure to regularly power Visionary on full health minions.
Due to the high slow and long duration of the slow from Ice Blast, it is often a good idea to get at least one rank early game to help get kills.
Nunu is a great jungler but an even better counter-jungler. With Consume, you can steal neutral creeps from the enemy jungler and easily return to your jungle route.
You can use Consume to heal yourself if a fight is not going your way, or to heal some health if you are trying to escape from an enemy. It can often help you avoid death if you Consume a unit while retreating.
Blood Boil has a 15 second cooldown and lasts for 12 seconds. It can be cast on an ally or minion (or just yourself if jungling) and you will still receive the same effect. You should try to always have the buff active.
Keeping Blood Boil active, you'll need at least 20% Cooldown Reduction.
Combine this with Ice Blast to chase down a fleeing enemy or escape a pursuer without a gap closer.
Use Blood Boil on an auto-attack based ally to improve their damage output.
Using Blood Boil on a cannon minion can dramatically increase your pushing power.
Using Blood Boil on a promoted minion can even secure a kill.
One possible effective skill order when playing Nunu as a support is to get one level of each skill, immediately improve Ice Blast to level 3, and max out Blood Boil as soon as possible afterwards. This leads to a good combination of harass and utility to make him a useful laning partner and contributor in teamfights.
Regardless of whether you can channel the ability for its full duration, your ultimate Absolute Zero is an AoE slow and attack speed debuff that can easily affect the outcome of a teamfight or small skirmish. Prepare to interrupt Absolute Zero early quite often for partial damage if an opponent is about to escape its range - in midgame, most characters can escape Absolute Zero completely if given its full channel.
Remember to take advantage of lulls in laning to grab neutral monster buffs with your Consume.
Absolute Zero is a devastating tool if you bait a fight into a bush. Unwary attackers can end up rushing into an ambush point or a shrub filled with teammates, being unknowingly slowed by your ult and becoming vulnerable as they are slowed or after the ult saps them of large quantities of health.
A fully channeled Absolute Zero with the addition of Consume and smite can completely wipe a buff camp in the jungle, making him a very effective counter jungler and buff stealer.
Similarly, Nunu can out-smite other junglers with Consume and smiting the buff afterwards if necessary. This is also a good way to steal The Dragon and Baron Nashor on Summoner's Rift, or Vilemaw on the Twisted Treeline.
The lore lists Nunu as a fighter, but he builds like a cross between a tank and a mage. Ability Power and Armor are in general Nunu's most important stats, as he needs high armor to survive long enough to build up Absolute Zero, and ability power for any real kill strength. Most Nunu builds are intended to make him very hard to kill and to keep him on the battlefield for very long periods of time.
Nunu benefits greatly from both Health Regeneration and Mana Regeneration - particularly Mana Regen, because Consume is a source of health. Using a Faerie Charm combined with Visionary lets Nunu use far more abilities than other champions early on. If desired, adding a second Faerie Charm to the initial purchase allows Nunu to cast spells and heal with Consume almost continuously without running out of mana.
If laning, Nunu likes to be tanky to be most effective. This puts Nunu very effectively in a role of bottom lane support, with both a single target and AoE slow, and single target haste and AS buff. With his high healing rate using Consume, a good Nunu player can absorb a tremendous amount of damage and still stay in a lane for a VERY long time.
As the game progresses to the teamfight stage, Ability Power becomes a crucial stat for Nunu. With defensive masteries, runes and a Rod of Ages, Nunu can be a team's tank without any tank items thanks to his high health gain.
Because Absolute Zero can be interrupted with a silence, stun, etc., a Banshee's Veil is a very useful item, blocking the first crowd control application and giving a better chance of completing the channeling.
Since Nunu has two skills that reduce attack speed, an additional Frozen Heart or Randuin's Omen can be used to effectively cripple all marksmen, as well as melee carries like Master Yi, Aatrox, Tryndamere and so on.
His laning phase is one of the hardest to counter, due to his spammable Ice Blast and his Consume that restores his health and gives him a single minion kill and his Visionary that allows him to stay in lane for a very long time.
Although he has high survivability he's mostly dependent on his Consume to stay in lane so mana starvation will render him weak. Constant harassment in lane will force him to use his spells when Visionary isn't active, so he'll be left with no sustain apart from Health Potion / Crystalline Flask. That can force him to tower hug or recall if you can harass him under his turret. Because of this, a champions with long range harass are a great lane counter. Examples are Caitlyn (decent range, and her Piltover Peacemaker can harass him under a turret), Twisted Fate'sGold Card can stop his ult and the range of his Wild Cards is high enough to easily harass him under a turret.
When you see an enemy Nunu going to a brush, take care of face-checking it. He might start channeling Absolute Zero if you get too close.