Detailed buying sequence should look like this:
Dorans Ring,Dorans Ring,Boots of speed,Sapphire Crystal,Blasting Wand,Rod of Ages,Sheen,Blasting wand,Lich Bene,Needlessly Large Rod,Rabadons Cap,Ruby Crystal,Negatron Cloak,Banshee Veil,Chain Vest,Guardian Angel. Ofcource you can always adjust to the situation but this is the safest way :) Btw u sell dorans rings when u r out of space.

In easy way :D
~Spam Ice Blast
~heal your self when needed with Consume
~Assist your Allied champion with blood boil when chasing and/or just smashing an enemy champion.
~Cast Absolute Zero in a Smart way (Bushes, Team Chase etc.) or Altairs Jump of faith way ,meaning on open team fight Result will be: wasted ultimate skill or Penta kill (maybe not but devastating crash to enemy team)

I like Nunu to be a Terminator from the beginning, so he never runs out of mana and hes survivability is high. (and a must for AP char, 15% magic Penetration).

going E,Q,W instead of classic E,W,E or E,Q,E is because I like to be agressive and tough at the same time ,also giving a good support to allied champion. Rest is yours to consider but, u have to maxout Ice blast as fast as you can, unlock Ultimate skill (R) at lvl 6,max out Blood boil after Ice Blast.

*Early
-At the begining you can spam with Ice blast harass enemy champions.
-When you hit lvl 3 you should always help out your laning partner with blood boil (if he is physical dps)
*Mid
-At lvl 6 u will get "Absolute Zero" it is good to use when u r in bushes, cos that way enemy cant see the spell casting. But u can show a bit of your cockyness by slowing them with dice and exhaust + some lane partner support, and then killing 1 or 2 feeders on your lane. (Important:be sure that enemy laners dont have any kind of taunts, fears or stuns at the moment when u cast absolue zero)
-Above lvl 8-10 it really depends on match what you are doing but, with your teleport skill you have a better control of the map, btw 3v2 with nunu in it is deadly for anyone.
*Late
-At this poit your job is to harass the hell out of enemy team with Ice blast, and remember to blood boil one of your ad allies before team fight or at early phase of it.
-Now absolute zero is always a gamble in open team fight but its good to use after the culimination of a team fight when your team is chased or your team is chasing :) When chased you can actually get couple of kills, when chasing it is allways a good slow and assist for your team.

~~Physical dps is a best choice.

So far I was feeling best with Warwick on the lane, because of healing skills, descent survivability, and big dmg. but u never know :) (your ww has to have some balls).

I think Squishy partners are not any good but, like I said it depends on your and your enemy play style and lvl of skill. (I like to go agressive with nunu)

(Xin Zhao or Jarvan should be a good lane partner also)

You propably get some kills at the laning phase k(1-5) depending on your and your enemy skills.
Later on team fights you most likely get a lot of assists a(5-10) but you never know, with Lich bene and blood boil you are still a pretty good finisher k(1-2). And at last, if God is with you when casting Absolute Zero you will get a lot of kills and/or turn the team fight in your teams favor.