Researching a freelancer's past experience gives you a good idea of his abilities. With that in mind, ask him directly for details of previous work in the field or, alternately, explain the assignment and discuss whether he is a good fit.
Research on your own the freelancer's previous work by using the Internet. This not only gives you a good idea of individual expertise but also can give you an idea about reputation. Successful freelancers tend to have either a consistent amount of work in one place or a large number of samples in several locations, so this is a good way of establishing their capabilities.
Finally, if a freelancer seems to be the right person for the assignment, make contact again. Email the freelancer and express your interest in working together. Give all of the assignment details, including word count, style templates or formats, and deadline, and agree on a price for the work. After reaching an agreement, email the freelancer a purchase order containing all of this information and an assignment number.