There are excellent Personal Trainers that believe in the value of education and work to consistently improve their skill set without formal degrees. These individuals are usually few and far between. One of the most important aspects is ensuring that he or she is actually qualified to do the job. It's all too easy for people to call themselves "trainers" when they have little or no expertise, no education or certification, or falsely claim certifications they have not received.
Good trainers have multiple certifications from several reputable organizations or degrees in the exercise or fitness field. The two Gold Standard and most widely recognized associations and their certifications are the National Strength and Conditioning Association (NSCA, which confers both CPT certifications and CSCS, or Certified Strength and Conditioning Specialist); the American College of Sports Medicine (ACSM), which confers Certified Exercise Physiologist.
Unlike most certifications, they both require significant prerequisites before being allowed to sit for the testing examinations. Always research the background and education of the people you are trusting with your health and wellness.