Trouble filling shapes

Hi everyone! I'm working on a state outline image, and am having a problem with using fill colors the way I'd like. I suspect I'm missing an obvious solutions as a beginner. The state outline itself is one path, and I've drawn five different paths across/within the state outline to represent water lines, mountains, and so on. I'd like to be able to apply various fill colors to the different shapes created by the intersection of these paths, but whether I join all the paths together or leave them separate, I can't seem to apply separate fill colors. 

Am I missing an easy solution? I can fill the entire state outline in one color if I select the whole thing, but can't seem to separate the shapes within the outline. Is there a way to redirect or segment the paths somehow so I actually have five individual shapes within that outline?

Thanks!