If you are arranging a cornet/ trumpet lesson for yourself or for a child It's good to talk! Don't be shy in asking any question, after all if you or your child are really going to enjoy these lessons you have to be comfortable with your teacher and have fun whilst learning. don't be afraid to ask any questions for example: 

How many pupils do you teach? How long have you been teaching? Do you have any references?

Make sure you definitely want to learn. All teachers should encourage their pupils but without the commitment and practice from you or your child it can be much harder. If you have chosen the right teacher you will want to practice and enjoy playing so it shouldn't be a chore.

Make sure you enjoy your lessons, it is ok to have trial lessons to find the best teacher for you. Make sure you talk about your musical interests, even if you like pop, rock or jazz, it will really help your teacher to find the best way of teaching you and help you learn to your full potential. The more open you are about your expectations and interests, the more useful the lessons will be. 

If you have arranged tuition for your child, you should continue to take a close interest in the progress being made. Make an effort to sit in on lessons once in a while and supervise practice. It is often very helpful to teachers to have the opportunity to discuss how your child's skills are developing. The most important thing is to be happy and have fun learning!