Questions to ask your prospective trainer: Is the trainer "certified"? Certified at what and by whom? There is, at the moment, only one certification process which is done by an independent organization. That is the CCPDT, or Certification Council for Professional Dog Trainers. It is an organization which has no affiliation to any dog training programs. This is important because when people go through a chain store training program, or attend a school to become a dog trainer, they pay their money and the school "certifies" them. A truer test of their skills and knowledge would be if they attended the school, then were able to pass a test by an independent organization such as the CCPDT. The CCPDT has a written test, a skills test, and a behavior test. That being said, it is possible to be a very good trainer without being certified by the CCPDT. There are many, many trainers who have been training for years, have kept up with current training techniques, and continue their education in the science of dog training and behavior, but just aren't CCPDT certified. There are also trainers who were CCPDT certified and, for various reasons, chose not to maintain that certification, and there's nothing wrong with that.
How long have you been training? This is sort of a trick question. Just because someone has been training for a long time doesn't mean they have kept current with their knowledge. They may still be doing the same techniques they learned when they first started but haven't changed a thing. The science of dog training and behavior has evolved a lot in the last 20 years, so if they haven't changed with it and are stuck in the stone age with their techniques you should look for someone else. A better question might be "What kind of continuing education do you do and how often?". Or, "when did you last attended a dog training or behavior seminar?", or even "what was the last dog training book you read?".
If your dog has a behavior problem, has the trainer dealt with this issue before? What was the outcome? If a trainer has been training for more than even a few years they have probably seen it all to some extent. The ideal answer to this question is "of course I've seen it and it all turned out great". Unfortunately, the outcome of a behavior protocol depends on the dog owner's commitment and ability to stick with the training. So, the answer to this question could be quite varied. Hopefully the trainer has seen more than one case such as yours and the majority of them have had good results. But if it's a tough behavior problem that is going to take a lot of work on your part, it means that would be the same for other people the trainer has worked with. So don't be too quick not to hire a trainer if they say one case didn't turn out well. The owner may not have been as dedicated to fixing the problem as you will be.
What training methods do you use? Ideally the answer to this is positive reinforcement, maybe with some negative punishment (we know, big words). Nothing with leash corrections or harsh alpha roll type stuff. If you are not sure what an alpha roll is or why it is bad, read the position statements of the American Veterinary Society of Animal Behavior. If the trainer throws around the words "alpha" or "dominance" a lot you and your dog should run the other direction.
Do you have protocols for specific issues and how flexible are those protocols? Most trainers have a basic protocol on how they deal with specific behavior issues. However, those protocols should be able to be adjusted for each individual dog and household situation. It shouldn't be an all or none situation. So, if they recommend something that won't work for you then by all means speak up! You are paying for their knowledge and expertise, but if you can't use it then it is worthless to you. But they won't know that if you don't tell them. Hopefully they will be creative enough to modify the protocol so you can use it.