Hello Everyone, I am PhoenixianSlayer. I loved the updated Nunu, so I played a bit of him and wanted to publish my findings.

Nunu is really cool and unique champ that focuses more on building team advantage by grabbing jungle objectives and enemy camps. Before the update, he couldn't do much else because his kit wasn't able to deal any real damage except through his ult which was hard to set up with that kit. His redesigned kit makes it much easier to get damage on enemy champs with some pretty good damage spells that all have some form of debuff on them, making it easier to land the one-shot ult.

Pros:

High impact jungle
A good gank is hard to avoid
Can Solo Drake at lvl 5 and Herald at lvl 8
Needs little if any help with Baron

Cons:

Weak Early Game Vs. Champs
his ult can be interrupted with CC
his ult takes time to get the full damage and is immobile in that time, so he has to survive 3 secs doing nothing in order to get the kill

In order for to use Nunu's abilities to the fullest, you need to straddle the line between tank and AP. Tank to survive until you can deal you big damage and AP so that the big damage is deadly. Resolve and Sorcery are the best paths to accomplish this.

Resolve Row 1:
Aftershock works the best as your main rune. Grasp of the Undying only activates on a basic atk on a champ. That is not going to happen as often as hitting someone with a snowball to activate Aftershock. Also, it activates after a period of time while Aftershock guards you during that time.
Guardian activates only if another ally champ is nearby (literally standing next or in you). That is rare, even for support mains and since you are roaming around, it is even more unlikely to work. Therefore, its best to find a rune that will always be active. Aftershock can be activated by 2 different abilities, so it's pretty good. It also gives you protection while you use Absolute Zero if you use it right after snowballing into someone.

Resolve Row 2:
Demolish ends up being the best rune on the list. Font of Life doesn't help you survive and does very little to help others survive (since you aren't building a ton of tank), so its not useful in this case. Shield Bash only activates when you use your Absolute Zero and you can't AA during that, so you can't make use of it.

Resolve Row 3:
Bone Plating is best because it provides some good damage absorbtion. Second Wind only helps you after you survive the battle Consume covers that function a lot better. Second Wind's recovery is insignificant and almost unusable in comparison to Consume. Conditioning won't add that much to Nunu & Willump since this build isn't that armor or magic resist intensive.

Resolve Row 4:
Revitalize is best here because it increases your heal and shield rate by 5%. This makes your Consume more potent, making it easier to clear camps. It also increases your shield from Absolute Zero which is a big increase since it is already equal to 30-50% of your bonus health. Unflinching is somewhat redundant since you have complete slow resistance during Biggest Snowball Ever! and the Tenacity isn't as helpful as the heal and shield increase. Overgrowth is better in a lane where a lot more minions are dying near you when compared to the jungle since the minions come to you in the lane while you have to travel to the monster camps in the jungle.

Sorcery Row 1:
My general experience is that Waterwalking is really handy with getting around the map to gank a lot. In addition, jungle fights occur in the river more often than not, so you have a nice damage bonus for the fight, or a speed boost for the flight should you start losing.

Sorcery Row 2:
Celerity comboes well with Waterwalking and Biggest Snowball Ever! so that is why it is a good choice. You get a lot of speed from the snowball, and if you prepare it correctly, you are getting a 150% damage ratio on that snowball, so amplifying the speed to make sure it lands is a really good choice.

The only other good choice for secondary runes is Transcendence. Its good, but not as useful as the other two

Call of the Freljord
One of your main camp clearing tools. It gives you AOE damage to take out camps with lots of monsters and extra damage on big monsters. Just make sure to hit the big monster in a camp first to get the passive effect. When ganking, this passive does the most in bot lane since it increases attack speed.

Consume
Makes taking out large monsters a breeze by hitting them with basically and additional smite. Also does plenty of damage to enemy champs which is nice considering it used to not do that. It obviously does a lot less, but does plenty of damage with some AP.

Biggest Snowball Ever!
Your main engage tool. You need to start it ahead of time and charge in with it once it has had full charge time and it maxed its damage. Be careful with your snowball once you are in lane because you want it to hit enemy champs and not their minions.

Snowball Barrage
Keeps Opponents from escaping once they are in your sights. It's like Taliyah's Threaded Volley, but its more like you burst several at once, hoping to hit all three and root the opponent.

Absolute Zero
An AOE nuke that takes time to charge. As long as you can survive to the end, they will all be dead. Also, you can't move or get hit with a stun or something that stops abilities or it will stop charging. You still get some damage out of it, but not nearly as much as you would want out of this ultimatum ability.

Smite: Mandatory for Junglers. Enough Said.

Flash: Necesary for lining up tricky ults or closing the gap with a giant snowball.

Barrier: Good for surviving to finish up an ult, but is unnecessary if you play smartly in the beginning and get plenty of cash to make yourself tanky by mid-late game

Main Ganking Combo:

W -> Q -> E -> R

Start with Biggest Snowball Ever! to stop them from moving for a bit, land Consume since it does a nice bit of damage and has the lowest ability range, then following up with a Snowball Barrage which should hopefully root the opponent. If you really need the damage and you aren't getting any help from your laners, use Absolute Zero

Ganking when Optimal to ult:

W -> E (Optional) -> R

Use Biggest Snowball Ever! to keep the opponent from doing anything as you start Absolute Zero and hope that they will stay put while your ult finishes charging. If they have a knockback, cancel ult once the knockup ends so that they take at least some damage. If they are mobile, use Snowball Barrage to root them as the knockup is ending. That should keep them in place for the early half of the ult and the extreme slow should keep them there for the rest of the ult.

The general jungle path I take is Blue -> Gromp -> Scuttle on that side of map -> other scuttle -> Red -> Raptors -> Krugs. Then I will back to get Skirmisher's Sabre. Next I will look to clear while staying near the lane that is struggling the most. Communicate with your team to determine which lane is best to stay by. Also, when possible, go for scuttles whether you need the health or not. They are good for vision and keeping a gold lead. At lvl 5 (with 3 upgrades on Consume) you can solo drake. Communicate with your team to play aggressively to keep their lane partners busy. It is best to go for drake if the enemy jungler ganks top. If you don't know where he is, make sure and ward a large radius around you so you can see him coming and request help if needed. You can also steal drake since your Consume + Challenging Smite = over 1000 damage, so you can steal pretty easily.
Avoid early 1v1s with enemy junglers since you don't have a ton of damage early on.