Some dealers that sell GE appliances offer repair services as well. One example is the home retailer Conn's. People who have purchased appliances there can contact Conn's to set up a repair appointment. Depending on warranty status, the repair appointment may or may not involve a fee.
If an appliance is under warranty, it's also possible to contact the parties indicated in the warranty paperwork to set up repair. For appliances that are out of warranty, contacting a reputable local repair company that services GE appliances is the best way to start the process. Using referrals from friends and looking at third-party websites that offer company reviews are two ways to avoid hiring an incompetent repair company.