Every personal trainer has to abide by certain industry standards in their profession.
This is very important to ensuring that the client receives the best training possible and that workouts are done in a safe and effective manner.
There are various bodies of certification that are going to have slightly different industry standards; however, all of them are going to emphasize safety and an ongoing relationship with the client. It is of critical importance that the trainer and client form a relationship of trust and open communication for the client to see success.
Furthermore, the industry standards should help you to feel comfortable knowing that the trainer you are using knows their information. If they are not certified by a major fitness organization then you may be at risk for getting faulty information and should take precaution. All the organizations, while slightly different, offer certifications that require a great deal of studying so that the trainer can create a program that will help you reach your goals. Without this studying, it is hard to say whether what they give you will actually help.
Don't be shy about asking your trainer whom they are certified with. You are paying good money to use them and need to be certain you are going to get the results you desire.