Do not be overly exuberate
Do not be a wallflower who does not associate with other students, but also do not be overly exuberate. Be pleasant and polite, but check your ebullience at the door. Do not make jokes or spout off when the instructor asks questions, or when in friendly conversation with other students. Just be one of the students and let your personality and effort speak for themselves. After a few weeks, you will have built up enough good will to let your true self shine through.
Find the leaders
As a new student, you will want to learn about the culture of the school, about what the instructor expects of students, and about what upsets or impresses the instructor. In any school, there is the way things are supposed to work, and the way they actually work. As a new student, it is up to you to find out this information without appearing to be prying or nosey.
Start out by determining which people appear to be plugged in to the happenings in the school. This may not be the senior students, as one would expect. Some people know what is happening, while others think they know what is happening. Seniority in a martial art class is determined by the belt rank, not by knowledge or leadership qualities. There is the “official” way something should be done, but the ones “in the know” know the way it should be done if you want to get it done quickly. Once you find the ones “in the know,” approach them with simple question about how the school operates. Do not ask direct personal questions, such as “Is the instructor a good teacher?” Instead, ask indirect process questions, such as “Does the instructor mind if students ask questions?” Chances are that the people you ask will add some of the personal type of information, so you will find personal information without coming across as being nosey.