That's the easy part actually. Some situations you just sort of memorize the odds for. For others there are short cuts to get to a good approximation (the percentage of hitting on the next street are the # of cards that make your hand x2).

The harder part is determining the range of your opponent's hands and factoring that into the EV. And then factoring in what your opponent is likely to do. So yes, it does get pretty complicated quickly. With practice though a lot of it becomes intuition.