There's absolutely nothing to winning the jungle and the game with Nunu, which is why he is so good.

As this is my first guide and I haven't got much to say, I'll keep this short and to the point.

~Penguin. :D

To start, you need to take the only risk of the game.

Invade the enemy jungle, and try to guess which buff the other team is starting at. Put a ward down, and then run out, whilst protected by your teammates or a support. Then, wait till their buff is at 1/4 HP, and smite it.

If they started red: Don't be afraid to enter a teamfight, you will most likely win with if you have their red buff, and should get level 2 from the kill.

If they started blue: Take a bit more precaution in what you do, and try to back off as much as you can.

Start at the opposite buff as to the one you've stolen, and then kill all of the creeps in that side of the jungle. Then, you might want to recall to purchase some of your first items, after this, take the same buff on your side that you stole from their side, kill all of that side's creeps, and then look for ganking opportunities.

Be careful of counter jungles at this time, as, if Nunu falls off, in the early game, he is more of a hinderance than a help to the team.

Keep following the previous steps, and keep ganking. If anyone is missing from their lane (dead/ganking), then fill in for them until they are back, and then resume jungling.

There should be a lot of teamfights in the late game, and a well placed Nunu ultimate is one of the most helpful things to your team at this time, with the AP you get from your item build, your ultimate, fully charged, should do somewhere between 1200-1600 damage, and slow the enemy for a long period, this will help your team maintain crowd control and the upper hand in team fights, along with your "E" ability.

P.S. If your team has scored an ace or a quadra kill, you can tank the turrets and end the game relatively quickly.