First of all, ask yourself what you want out of boxing training. Do you want to lose weight? Are you planning to enter competitions? The answers will help determine what type of training you want and need.
The coach should give you general information about how the gym is run. Does he or she run the place like a formal gym class where there are certain objectives to be covered each day? Will the coach give basic instruction for a few weeks, then turn the participants loose to craft their own workouts? Is it a cooperative atmosphere where everybody in the gym is willing to give out tips to help everyone else?
You should ask what the coach's expectations are for the people who train under them. A friend of mine went to a gym where the first thing the coach asked was, "Are you going to compete?" Some coach's ideas of training mean having nothing but winners in the gym and all the glory that goes along with that. Check the gym's walls for the amount of trophies and belts being displayed. They might not discourage you from joining, but if you only want to do the workout, they may not spend a lot of time interacting with you while you're in the gym.
Find out what the policy is regards to sparring. The trainer at the first boxing class I took wanted everyone to spar each time we were in there. There were a couple of women who signed up together for the class. They had brought what looked some expensive gloves to use on the bags. When the woman learned they were expected to spar, one of them said, "You mean we have to get hit?" They dropped out of the class after that night. I often wonder what they did with their gloves.
Another former coach of mine only allowed us to spar once a week. This was at a municipal boxing gym where sparring was an option of boxing training, not a requirement. The coach also told new people to let him know if anyone was trying to pressure them into sparring if they didn't want to do so.
Observe how the coach works with the fighters in the gym. Is the coach hands on? Does he or she interact with all of the fighters, watching them and giving them pointers on technique? Does the coach spar from time to time? Does the coach hold the punch mitts for people? Or does he or she sit mainly on the sidelines and give orders? The answers to these questions will determine what you want and expect from boxing training.
Don't be alarmed if you hear the coach yelling or even cursing at people, especially if they are monitoring people who are sparring in the ring. It's nothing personal, and a normal part of boxing training for some coaches. The coach's job is make sure people are focusing and executing proper technique. Throwing sloppy punches and having other bad habits techinque-wise is not going to help the boxers, especially if they have a fight coming up.
Here is some more information about what coaching involves.