At some point every business can benefit from hiring an in-house designer or a freelancer for random projects. Typically a Graphic Designer job posting will get resumes from print designers, where as a Web Designer posting will get resumes from just that web designers. So for starters titling the position correctly will get more relevant applicants.
Whether you have had good, bad or any experience using a designer the truth is you want to know how capable the designer is for your needs and how much they cost.
First to find out how capable a designer is you need to know what software they work in, the standard design software is Adobe; Illustrator, Photoshop, InDesign, etc. Anyone that works in Corel or other programs is not going to deliver an industry standard product which will cost you down the road. The industry used to be Mac only but PC is just as capable these days with no difference in software capabilities.
Second you need to see a portfolio to truly understand the capabilities of the designer. If a designer doesn’t have a portfolio then pass, even a student will have some sort of portfolio to showcase their work. In addition to asking to see the portfolio ask how the designer participated in each of these projects. At times there are collaborative teams and the designer was part of a team. They do have the right to show the piece since they participated on the team but does that mean they can handle your project, not always.
When examining a portfolio look for balanced design with clean layouts. Does the color scheme work well? Are the designs organized in a way the creative is easy to read? is there a visual hierarchy that sells the product.
Finally you need to know how much the designer charges. You can go by an hourly fee or after discussing the project you can ask for a quote for the entire project. It does depend on the type of project and the part of country you are in but expect to pay $25 to $60 an hour for graphic design. Find out if the designer has any specific payment terms. Usually smaller projects are billed at the end of the project and larger projects are billed out in phases.
Remember you get what you pay for. If you choose to go cheap and hire a student to do the job of a professional you will get student work for your final product. Which could cost you more in the long run.