How would you go about modelling this kind of hair?

Make a hair particle system and use the comb brush. Might be too realistic, but you should be able to change the material.

I was thinking you model the base shape then ass the strands after, but I'm finding it a bit awkward. Any tips would be good. I'm not looking for an exact copy, but more of a cartoony or anime look.

I have found that some people like to model a basic shape of the hair using large planes going over each other (kinda like feathers, but wider) and then either paint hair onto it with an alpha channel or just using an already existing hair texture. Alternatively you can make realistic hair using hair particle systems.