Nunu is an amzingly good hero. You don't need to get a lot of kills, but he wins games.
Here's my strat, won 8 games in a row with it. lvl 14 summoner.
Spells:
Teleport / Smite

First item: meki pendant.

In the beginning, tech consume and stand near some creep spawns. You can smite/consume early, gain some easy gold, and have consume cooled down for the first wave of creeps.

Consume + pendant allows you to stay in lane no problem, smite and consume creeps and you farm terrifically.

You only need one level of consume, maybe two if they're harassing you badly.

After that, two options:
If you have an Ashe or a Jax that is doing well, blood boiling them all game wins the game.
Nunu is a one trick pony, his ult OWNS.

If you can pull it off!
So, if you're playing a chogath or something, it can be tricky.

But, just keep stacking ability points. Make a philosopher's stone, then:
sorcerer's boots
mejai soulstealer (really helps - you'll get lots of assists with an AOE ult anyway)
rylai's sceptre
abyssal sceptre, etc

you don't need health regen due to consume, you don't need mana with a philosopher's stone (free gold helps too), nunu is pretty fat so he doesn't need much to tank (rylai does it), and if you can pull of your ult in team fights, you can take out 3/4 of weak heroes health or 1/2 a tank. Not only is that absurd damage, but when you start up your ult, the only thing people can do is flee or try to stun you (continuing to fight your team is suicide), so you've essentially got an AOE stun for free. That, and you blood boil your MVP = gg.

If you're fighting a debilitating amount of silence or stun, this strat won't really work. But, you can successfully avoid most stuns and pick off people in the middle of a team fight - you don't have to start with the ult.

This will result in lots of scores along the lines of 8-5-20.

I recommend defensive and utility masteries. You don't need attack for Nunu you just need the ult and a team.

I lol'd, because I went on a 9 game winning streak of normal games with Nunu. Each game, I was responsible for roughly 25-30 enemy deaths with Nunu's ice blast. Nunu doesn't shine like the top heroes, but he's an incredible support champion. My friends were hung up on "Tier Lists" and threatened to play only "top rated" champions, but I showed them how powerful Nunu can be in a team game, and since then they've reconsidered.

Anyways, Nunu's item build can be a bit challenging because he's a hybrid tank/support, but in my experiences, here is my nunu build:

1 - Meki Pendant
2 - Boots of Swiftness
3 - Catalyst of the Protector -> 4 - Rod of Ages
5 - Nashor's Tooth

Ever since I realized his power, Nunu has become my most favorite champion.

Nunu is not the second worst hero in the game, over 80% of the games i play with Nunu i come out with highest amount of kills. I go for AP build
Trinity force first
Then Greaves
Nashors tooth or Rod of Ages
Rageblade

Nunu is the name of the boy that is riding the Yeti, hence, Nunu the Yeti Rider.

Also, the Yeti's name is Willump, and is clearly stated to be male.