I am not a designer, but I have been in your position. I got lucky enough to get randomly assigned to a roommate who is a graphic designer so I keep him in my back pocket. But I have also been very happy with elance.com. There are other sites that do similar things as well.
One elance you can look around to see what closed projects bid price was, try to find something similar to what you want to do and look at the price, this should give you a good idea of what you should expect to pay.
I would ask the designer to show you previous work that they have done as there isn't any specific qualifications to look for in designers. If you are the sole person working on the project then make sure you pick someone whos work you like. If you have anyone else that is invested in the project go ahead and get them to tell you which ones they like the most.
You also will want to check with them about how much of the work in their portfolio they have actually done. Some of the not so honest ones like to say they worked on some site, but in reality they where either a secondary designer or only did one very small part of it.
It is very typical to require the designer to sign a Non-disclosure agreement before you give them any specifics of your business ideas, but it is a good idea to let them know what you have in mind so they can take everything into account when designing.
