In the field of dog training, there are no "requirements" to call oneself a dog trainer. In addition, there are many ways to train a dog, as well as many different fees. So, how does an owner decide on a trainer for their dog?
First, you want to look for a trainer that uses positive-based training methods. There is a lot of talk these days about being "leader of the pack". While there is some merit to this, it is the sign of an old school trainer who insists on this mentality. We get dogs because we love them for what they are. We just want them to direct their desires through appropriate channels. For example, we want them to potty outside, chew their own toys, walk calmly on a leash, etc. Training is a way we communicate with a non-verbal species. Learning is motivational. For a dog to want to learn, it should be fun for them. Give them a reason to want to listen to you other than punishment. There is no need to jerk a dog on a leash in order to teach them how to behave. For the most part, owners want their dogs to be part of the family and a good canine citizen, not a robototic animal that is afraid to romp, play, and be a dog. Punitive methods can create a dog that is afraid of you.
Second, what is it that you wish to accomplish? Basic manners? Housetraining? Does your dog have anxiety, fears, or aggressive issues? You need to select a trainer that is skilled in your area of needs with the proven experience behind them. Price is not the factor that should be your first concern. Most trainers can put together a program that will work for you within your budget. But remember, a dog is a life-time committment. The money you spend now on training will provide you with a companion that you will enjoy to spend time with. Amortize any training fees over the life of your dog and it comes out to very little per year.
Ask a trainer how much experience they have. Ask where they learned their trade. Trainers with little experience typically charge less because they want to use you to practice on. You would be better off spending a little more and getting more in the long run. Dog training is not brain surgery, but it does require a knowledge of learning theory and conditioning techniques and nothing says success like hands-on experience with lots of different dogs.
Ask if you can watch a single group class or training session. A trainer that you want to work with should have no problem allowing you to do this. Also, ask for references and call them. Ask a trainer what happens if s/he is unable to keep a scheduled appointment or if a training technique is not working for you. What if you and the trainer do not "hit it off"? If you are working with a single trainer, you typically have no options as most do not offer refunds (this is standard in the industry). If you are working with a training company, you have the option to work with a different trainer, plus there are a multitude of resources behind your trainer.
Do not be afraid to ask questions. It is your dog, your companion, and your investment. You have the right to make the right choice for you.