Research potential reps by asking artists you know who they deal with, looking up agencies online and checking directories put out through groups like the Graphic Artists Guild. Always check to make sure they are looking for new artists, so you don't waste your time or theirs with unnecessary mailings.
Send out some samples of your work, or if they accept digital submissions, a link to your online portfolio. Check their website or directory listing, if available, for their submission guidelines--and follow them to the letter to ensure your submission gets a fair look.
Ask for references of the agent, both of current and former clients, and contact them to get a better opinion of the representative, and if applicable, why the artist ended their arrangement.
Understand that, unlike literary agents, there may be some costs involved with doing business with an artist's representative aside from their commission. The artist is expected to pay at least a portion of the advertising costs associated with soliciting work, as well as paying for or providing portfolio items as well as postcards or other promotional materials. The split varies from agent to agent, but it's not unusual for the artist to cover up to 75 percent of these costs.
Look at the type of work the agent handles and how it relates to your desired market. If you're a new artist open to anything, this is less important than someone who's cultivated a certain clientèle on their own or has settled into a preferred style or subject matter.
Examine any contracts you are offered thoroughly, enlisting a lawyer if possible, to make sure you are comfortable with all of the provisions included. Ideally, the contract should benefit both you and the agent equally, but know what, if anything, you are willing to give up in exchange for the representation of this agent or agency.