Ask to see the illustrator's portfolio. An illustration is entirely visual, so you will discover very quickly whether or not you like the artist's style by viewing some of their work.
Negotiate with the illustrator to get an agreeable rate. If you're working with a freelancer, their prices aren't necessarily fixed and they will likely offer a better price if they feel that your project is a good opportunity for them to showcase their skills.
Before the project or job begins, be very clear about your expectations.