Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
The Nunu AP Build
In the beginning, you definitely want survivability and good damage output so I recommend always getting Doran's Ring. You want to start getting as many minions dead as possible and harass the other team with your Ice Blast. It is a very powerful weapon and can be free if you get 7 attacks on minions, so it's free harassment. As soon as possible, you want magic penetration so you want the Sorcerer's Boots. More magic penetration, the better. I suggest then saving up for the Abyssal Specter as it provides three great tools; more ability power, more magic resist, and magic penetration. these become especially useful when you get your ultimate ability. You still want to make sure that while harassing, you have plenty of health in case of a gank, don't forget to consume your minions for more health. After that I would highly recommend either the new item Morello's Evil Tome for ability cooldowns, ability power as well as mana regeneration. Great new tool; you could also switch that out for a Nashor's Tooth, but that's up to you. You could always use more attack speed for your Blood Boil, more melee damage output is great. Either way, it's up to you. Of course you want more ability power quickly so you should start saving for the Rabadon's Cap. Afterwards you want lich bane for more ability power, movement speed, and of course having massive melee damage after using your Ice Blast. After you have filled your inventory, I recommend selling Doran's Ring and trading up for Archangel's Staff, if the game is still continuing. Archangel's is a great item for mana regeneration and plenty of ability power. At this point, you're going to be a pretty ridiculous Nunu as you can put out more than 2200 damage with the ultimate alone. I highly recommend this build as it has never stirred me wrong.