First, what do you want your dog to learn?
Does your dog have behavior issues such as anxiety, fear, or aggression? Then basic obedience will not be enough. Some dog trainers only teach obedience, others only offer behavior modification, while some do both. Be sure the trainer is able to help you accomplish your goals.
Check out qualifications and experience.
There are many gifted dog professionals out there who aren't certified, and yet there are many certified trainers who are not experts.
It's best to look for those who have taken the time to become a true professional through schooling and/or certification, ensuring that they have had to pass some minimum requirements, do some studying, and put in some hands-on hours with dogs. Know also that new methods of training dogs are being discovered all the time, so good dog trainers will continue their education by attending workshops, seminars, and conferences.
Look for reviews and examples.
It is best to search review sites such as Google, Facebook, or Yelp because businesses can't pay to alter or remove reviews. To avoid being misled or duped, be sure to check the integrity of both good and bad reviews as some good reviews could be fake and negative reviews might come from their competitors. Many trainers share videos of dogs they've worked with on their website or on social media such as Facebook, Instagram, or YouTube. If not, ask to view a training class.
Be sure you're included in the training.
There's nothing wrong with board-n-train programs so that trainers can work through your dog's more challenging behaviors,
however it's important they also work closely with helping you to ensure your dog's success and prevent your dog from reverting back to old behaviors. More often than not it's the owner who needs the most "training."
Finally, your own philosophy and ethics.
Some people are opposed to certain training tools or methods. I am fine with most tools as long as they are used correctly and humanely. If you feel bad and object to a training tool, your dog will have a bad experience with the tool. A good dog trainer will be able to explain what they use and why in a clear way that you can understand. When it comes to choosing the right trainer, make sure that the trainer you choose agrees with and supports your own values, because you are the one who is going to live with your dog. If you feel that a trainer isn't for you, or your normally friendly dog is very reserved around a trainer, you may want to pass and meet with a few others.
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