After about 8 years of teaching, I've found that there's still much for me to learn on how to quickly build rapport with a new student. Also not having a particularly bright or bubbly personality makes it a little more challenging for the younger kids to start opening up in class!
Below are some simple tips I've found to be helpful with the students I've had in the past.
TIP #1: ENTHUSIASM!
If you are able to show the student that what you're doing/talking about is fun, exciting, and important, the students (and observing parents) will generally buy into it. Don't just show you're knowledgeable or skillful in the instrument; show you're passionate to teach the student.
TIP #2: GET TO KNOW YOUR STUDENT
Hold off on talking about the instrument or yourself. Get them to talk! Find out what they're interested in, why they are learning the instrument, etc.
TIP #3: INSPIRE THEM TO BE MUSICAL
Although some teachers disagree with me, I feel that performing a little something at the end of a trial lesson can really help the student see what the instrument is capable of, or witness the art of performance. But, inspiration can come in different forms. If the student likes facts, talk a bit about the developmental and neurological benefits of playing a musical instrument. If the student is a planner, map out what the musical journey is like, and what long-term goals they can set. If the student has a low interest in music, try and weave in the relevance of music in whatever the student is interested in.
Here's a more comprehensive list: