As Sparki said if you stay on the Beach East of Waimea but West of Sunset you could survive without a car i guess, but for me id say you want a car. That way you get to travel around and see the Island. Loads of spots to surf all over and some really cool things to see. Car will also make it easy to get down to Haleiwa were loads of great food is available. The busy breaks could have 30 plus surfers (and really good surfers) but not too far away you could surf spots that will blow your mind still with only 5 people out.
Most of the population is touristy but in reality other than surf, the other tourists are often their just to watch the surf. I did notice buses and but i think if they run on Hawaiin time you could spend most of the day sitting on one or waiting for one. Seems to hot to ride any real distance IMHO.
I guess a scooter would work well if you travelling light, but i didn't really see people with boards on scooters.
I would say when the Comps are on it would seem like a circus. It would be unreal to see first hand, but the place will grid lock like nothing and parking will be almost impossible, so i guess in that case, you may have to walk or bike.
You will want boards longer than you think, and you will want to be paddle fit, as many of the breaks are a long way off shore.
But it is a absolute must IMHO. The North shore is simply a surfing hot spot that needs to be experienced. Ive only been once and i can't think about anything else

We stayed on the beach, at a spot call Leftovers. I had the family in tow and they like me, they will talk about nothing other than the North Shore

Ask straight away at Foodland for a discount card. It will save you heaps. Eating at restaurants you can often split meals if you want to save. I saw one group splitting one plate between three people the serves are that big.
Embrace Acia bowls and Shaved ice.

Dollar at $0.82 exchange though will hurt the pocket..