How long have you been in business? This is the first question to ask. You don't want to be a guinea pig for a school. If this is the first or second year of operating for them, keep looking. I know someone has to be first and you are probably going to get a lower tuition rate but it isn't usually worth the risk. Running a training school isn't for the faint of heart. There are lots of lessons to be learned. Why let them learn those lessons on you?
How many people in the program I'm planning to take have found jobs in the last year? A good computer repair school will be happy to provide you with numbers. Even better is if they are willing to provide you with references including names and phone numbers. Unless you plan on opening your own business, knowing there will be a job for you at the end of your training is important. Don't overlook this part of your research. If they give you names to call, call them. While you have these references on the phone, ask them about the school. What they liked and what they didn't like. Better yet, ask them whether the training they received from the school was worth the price they paid for their training.
How much real life experience do my teachers have in the field? You don't want to get theory only. You need some practical advice to go along with that theory. Sometimes, you may find their practical advice being worth a lot more than their theoretical knowledge.
Why should I enroll in your course of study over another training company's program? Asking this question can help you identify the particular strengths of the training school you're examining. Keep in mind though that the answer to this question will usually be a sales pitch. Do some outside research to verify any information the school gives you.