i'm not an illustrator my self, but i think web design/dev is similar.
You charge either a flat rate that will definitely cover the amount of time you think it will take you (plus a little extra in case there are problems) or you can charge an hourly rate, and give the client an estimate of how much time it will take.
What should that hourly rate be, in either case? At least $50/hr, probably 90% of professional illustrators charge more too.
Plus, things like rush orders can up the price quite a bit.