Choosing a trainer that uses positive reinforcement allows you to build a strong bond and create an confident and eager worker willing to take risks during learning. A trainer who understands how to correctly apply the 'quadrants and principles of operant conditioning' will help to ensure they understand how to break behaviors into small enough steps so your dog will be successful at each step. Dogs that get frustrated or who are punished (corrected) typically shut down and do not offer the creative and intelligent behavior choices a service dog will need to offer during his/her career. Look for an "About" page on their web-site. It should outline their training philosophy and techniques, maybe even mentors.
Have they taken training or been certified by a recognized organization? Are they a tester or instructor for any? Which ones?
m) Can they tell you what "underthrehold", counter conditioning, systematic desensitization, Behavioral Adjustment Training (BAT), Look at That (LAT) mean?
q) Ask what training tools they use. The use of non-restrictive body harnesses are preferred. Head halters need to be specifically conditioned on the dog and they train you to use them properly avoiding jerking or lifting in their use. A flat collar is used for tags. R+ trainers will not use choke chains, prong collars, electronic (shock) collars or harnesses that tighten on the dog like front clip harnesses. Watch how they use the tools. A leash can be used aversively by popping or jerking, or can be used as an emergency back-up only. The latter is what you want to aim for.
7. How big are the classes? Smaller is better. Classes of 4 to 6 dogs is ideal to start. Larger can be chaotic, even if there is more than one instructor. If they have 12 or more dogs in a large space, even with a second trainer, it probably isn't the class for you as you won't get enough personal interaction with the trainers and it is harder to see and hear and understand in larger classes with the instructor standing far away especially with poor acoustics. If this is the only option, start with private classes so you and your dog already know the behaviors before taking group classes. That way, you can work on using the class to add distractions, rather than having them work against you while learning new behaviors.