Go onto https://dribbble.com and scour the place for quality design work. Once you've found some great pieces, look at what else those designers have done.
If their portfolio fits well with your requirements, contact those designers and tell them about your project.
Avoid sites like 99designs.com and oDesk in my opinion.
One of the most important question you need to ask yourself is do you want "production level" work meaning you give a specification document to a person and they create a piece of software for you or do you want more of a facilitator, in which someone works with you and uses their education, experience and coaching experience that will enable you to produce software that not only addresses the here and now but will benefit you in the future. Make sure you have it clear in your mind what exactly do we want this person to do for us? , and how does this align with our project, business and user goals, plus primary and secondary tasks?
I would build on top of Danny Halarewich's answer.
Having gone through a sorrow experience with Dribbble, I would recommend you also check that the work of the designers you contact is live, so that you can require them to send some references.
Reach out to those references before deciding on a designer.