Playing as Nunu once you hit lvl 2 you want to keep harrasing with your E (Ice Blast). If your HP is low you want to use your Q on the minion or jungles it depends on where you are. Being Nunu before lvl 6 in the gank you can't do much, try to make your enemy focus you and use your E on the enemy, use your Q on the minion in the gank. Once you hit lvl 6 make find a good circumstance to use ur ult. Be careful of the stun, fear, knock up, and etc that interrupt your ult. Do not release your ult, try to make it as long as possible, the longer it stay the more damage it does.

Runes is very depend on the map you play. In 5 for sure they will have a tank, so you want to use megic pen. In 3's you can just use flat AP it'll give you more damage on the enemy.

For the mastery I just use AP and a little of mana regen so it will let you harass your enemy. Remember the more you harass them the lower lvl they got, because they can't stay in lane, or you will gank them and get the kill, or you can go jungle fast with your consume.

In 5's you want to go more tanky because Nunu can't do much beside his E and R. So if you go tanky so you can just ult it once your enemy used some of their cc. In 3 you can just go for ap. Remeber tanky nunu can just ult for the team fight.

If you stay in lane just use you E first, but if you jungle use your q first it will heal you. remeber don't use your q directly. you want to auto attack first then use your consume to heal you to the max hp. you want to max your Ice Blast first to keep harassing your enemy. Remeber to max your ult at lvl 11 and 16.

As playing in 5's you want to go a little tanky so you don't need esc. Just with you W is enough.

Nunu is a really good champion for harassing and support your DPS with your W in the gank.

Harassing/Mana
Healing/not much damage beside the skill.