I am a personal Trainer, so I can tell you what to look for.
First of all, you want some body with the right credentials: certifications and experience. Do a google search for personal trainers in your area, ask friends who may have trainers, go to some private gyms in your areas and ask about their private trainers. Once you find a few trainers you like, ask them if they wil give you a free session so that you can try them out- most good trainers will do this. In the first session this is what they should do- If they miss any of these things, they may not be a good trainer. They should do a physical readiness analysis to find out the general level of your health and any injuries. They should find out your goals and establish a time frame for you to reach your goals- and a plan of action to reach those goals. They should look for any muscle imbalances and describe how they are going to improve them. During the work out, make sure they are totally focused on you and that they can describe why you are doing a certain exercise. Most personal trainers will want to train with you for months and months because it is good money for them. A superb trainer like myself will be able to get you in the best shape of your life in one month, training three times a week. At that point you will have all the knowledge you need to keep going b yourself and if you want to keep training with me after that, it is purely because you enjoy having a coach and somebody you are accountable to not because you still need a trainer. Those are the basics of what you should look for.
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