If you invade Nunu, do not fight him when he is near a jungle camp as he can use Q to gain a health advantage. Ideally, fight him when he is in the river or not near a camp.
Nunu can easily solo the Dragon at level 4 and after. Be prepared for this by having the Dragon warded at all times and by always taking the bottom side Scuttle Crab.
At level 6, Nunu can channel his R. When he does this, make sure you cancel or interrupt it. If you can interrupt his channel early, his R will not deal a lot of damage and it could save you or your allies life. Cancel his R with CC.
When it comes to securing an objective like the Dragon or Baron, never go for the 50/50. Because of Nunu’s Q, he will win every battle. Try to take the objective when he is dead or on the other side of the map.
Nunu is rather immobile when it comes to team fighting (once the fight has started). Lock him down with crowd control and kite him during the team fight so he is unable to be the frontline and get on to your carries.
Do not clump together when it comes to team fighting. If you stand close to one another, he will use his Snowball W to engage from afar and run into the enemy. If you are all close to one another- he might be able to get a 5 person knock up. Instead, group but not too closely.
Nunu is an early game dominant Jungler and will be looking to gank as much as he can.
Once Nunu hits level 6, his kill pressure and ability to gank increases thanks to the CC on his Ultimate R. Ward your flanks so you can see him before he is able to get to your lane and kill you.
Nunu has really good objective control throughout the game. Make sure you keep the objectives warded at all time so you can see him do them.