There is one main combo: run towards the enemy with your W, then start E while AA them. When the enemy is about to be Rooted and is inside the area, use both Q and R (but wait until the R is at its fullest, so as to maximise the damage). Use the shield that R gives you as an advantage, as many players do not realise that it scales with ap, meaning you might have up to 1.5k of shield if you are fed.

Funniest combo (in my opinion) is to wait on a bush and ping your team to lead the enemies there (your R is invisible when inside a bush, but it stills slows people). Just start casting the R while they are coming.

Start with W, and if the team can and wants to invade, wait 3 seconds on base and then go towards the invasion. If you are on blue side, start W on the bush near raptors; if you are on red side, start on the entrance of jungle beside wolves.
Whether you invade or not, go behind the tower, and when the minions reach the middle of the lane, start the snowball and go for the 3 caster minions, then farm the rest. Repeat, and as soon as you farm the wave with lvl 2, look for a roam. If you decide to go roaming, lvl up E, otherwise, lvl up Q and keep farming. Use Q to sustain in lane or win trades with W. DO NOT overuse it, as you have little to no mana. You should try to help your JG in every gank they do or roam when you see the chance. REMEMBER that if your team does not get fed in the early game, you are basically useless.

Here is where you'll start to get behind, unless you have dark seal, in which case you might be able to stay relevant until late game. So, the best you can do here is to try to be the one who starts the fights, or pick up squishies on the sildelines with your combo.

This is the part where you are practically useless. If you build the Feed Nunu Build, as you can't cast R due to how squishy you are, the best you can do is to start a fight and immediately use Zhonias so that your team can come and help you. If your team is not fed, then you probably have done a bad job in early game.

If, instead, you build the Behind Nunu Build, you become a tank that starts the fight and peels the carries in your team so they can do max. damage.

Have you played correctly, and your team cooperated with you, Nunu is one of the most fun champs to play.