I want you to watch the video below from someone I used to train with (or at least at the same gym). Anna is a very talented athlete and coach, and is noted for her feats of muscle control, performing advanced calisthenics movements in what seems to be an effortless manner. She also happens to be very well spoken, and in the video below she touches on a training aspect that anyone paying for coaching/personal training should be aware of. Check it out! (copy and paste the link, I'm still learning to embed videos)
First off: Hallelujah someone said it! That, and she said it perfectly!
Over the years, I've met handful of good and bad coaches across a variety of sports. From CrossFit, to Weightlifting, to general personal trainers; I've been blessed to find some great coaches, and some bad ones (because I've used those as learning experiences). When I met Anna several years ago, it was in a CrossFit gym run by a guy who honestly wasn't a great coach (great person, but coaching wasn't for him). But good coaches always have an answer to the following questions, and therefore, they are questions you should be asking.
1. What is the goal for today/this week?
A good coach (or personal trainer) has a goal for each week, or even each training session. A great coach will make sure that you know what that is. Weekly goal setting means you're not going to get something random from the coach, that has no direct correlation to your personal goals. The coach's weekly goals support your personal long term goals. If your coach isn't willing to tell you the goal, they probably don't have one. If that's the case, start doing your research into exercising for your goals.
2. How does [this] exercise fit the into the goal?
Again, a good coach has goals, and programs for those goals. They should be able to tell you what the effect of the exercise is in a way that makes sense, so that you can know what you're paying for and how focused on your goals they are.
3. How does this exercise/workout work?
Good coaches know how to communicate the science in simple ways. This question is a challenging one, because some coaches can talk your ear off about science, and have every bit of it go over your head (and maybe their own). A good coach knows how to explain a complex effect (such as the physiological changes your body undergoes during exercise), and make it simple enough for anyone to understand. The unfortunate thing is that some people know all of the science and can't put it into action, and some people know how to put science they don't understand into action.
4. Can we do something different?
Good coaches don't stop learning, and embrace new challenges. Maybe your coach has you doing something that you don't feel comfortable doing (eg, trying to have you do box jumps when you don't have the confidence yet)? A bad coach will make you do it, while a good coach will meet you where you're at and find a different way to achieve the same effect. And if the coach says no, revert back to question 3: make them explain why!
Long story short, there should always be an open line of communication between you and your coach. A good coach knows how to plan for your goals, communicate that plan, why that plan will work, and is also open to trying new things (if the thing makes sense). If your current coach doesn't possess these traits, it may be time to question their long term ability to make you better.