I find out what their goals are and what their preferences are in the way we reach those goals. This is initially done via their filling out paperwork which tells me about these things in detail. Then we work out together a path to get them moving toward the result they are after.
I am a licensed physical therapist and have treated sports and orthopedic injuries for over 35 years. This experience allows me to not only train around and help you overcome any orthopedic issues you may have, but avoid getting them in the first place. I am also certified with the Functional Aging Institute. This additional training helps me address the special issues that people have as they get into their 40s, 50s and beyond. Many people begin to gradually lose mobility and function as they go through the aging process. This begins as maybe a little added weight, maybe a little loss of balance/coordination etc. Often these things are imperceptible in the beginning. Allowed to progress though, they may lead to a loss of enjoyment of life and even a total loss of mobility. These things can usually totally prevented with a well designed exercise program.
I would want to know if the person who I'm about to engage in a process with that can have a tremendous positive effect on my life is a life long learner. If asked, they should be able to give you at least 3 or 4 names of people they either read, listen to podcasts from or study their courses on a regular basis. This tells you a couple of things--1) They are always trying to get better at what they do. 2) You can then look into those people if you want to and I find out quite about about how this person you are talking to will work with you. Do the people they learn from work with people like you? If not--ask the coach about that. For example, I study the material of several sports performance coaches. Someone who is in an older age group might question whether I would be a good person to work with them based on that. If they ask me about that, what I will tell them is that many of qualities one loses as they age- strength, power, balance, coordination, etc. are basically athletic qualities. The same principles/techniques used to improve these qualities in athletes are also applicable to people who may be a little older--just perhaps at a lower level of intensity, lower volumes, etc.