Your local community or trade college should have relevant programs in small appliance repair. Some classes you may want to look into are basic electronics classes, as well as classes in soldering and basic engineering math. You may also be fortunate enough to live near a community, trade or technical college which has a special program for fixing small appliances. Get a course catalog from your local community college and see what they have to offer.
Correspondence schools allow you to learn small appliance repair from the comfort of your own home and at your own pace. Such schools have the benefit of being cheap and structured around your schedule. However, they do have the drawback of not having an instructor or other students to draw from. Still, for the busier student, correspondence education could be the only realistic option.
Similar to a correspondence school, but without all that messy snail mail communication, an online campus is an excellent place for people to learn small appliance repair in a way that works around their already existing schedule. Online courses are also different from correspondence schools because of the greater degree of interactivity. You have forums where you can ask the instructor, as well as your fellow students, what you are not getting or doing wrong and expect a timely answer.
Whatever training you receive from whichever school you choose, your real training begins on the job. Nothing substitutes for the training that you receive from experienced professionals actively working in the business. Call around to local small appliance repair shops and see what they have to offer in the way of training. See if you can get in on an apprenticeship or part-time basis if you don't have the experience for regular full-time work.