For newcomers to Traditional Martial Arts (TMA) - Welcome. I hope you have first well researched and taken some free or discounted classes at different schools. You need to do this to see if you like and are are willing to spend a good amount of your personal time with a TMA style and instructor. If not, I suggest you read this article on what to look for in a TMA school. If you see this guy, run.
What do you do after you pick a school and instructor you like? You should get some type of written or oral explanation from the instructor on expectations and specific behavior in the dojo. Follow them If you are in a respectable school, these rules are geared toward your safety, self-control, respect for everyone, and learning. If there are higher ranks of students in the class, ignore them, unless they are teaching part of the class or demonstrating with the teacher. Keep your eyes and ears on the instructor and yourself.
You are learning your new style from the teacher or sensei, so you need to focus on him or her. As you learn from your sensei, watch yourself. There should be many mirrors in the dojo. They are there for you to watch yourself when performing katas and practicing techniques.
Most importantly, go at your own pace. Never try to rush through an exercise or kata to show how fast you are. There's a 100% chance you did it completely wrong. Everyone is different and we all progress at different rates. Go at a rate you are comfortable with and can do. This is about you learning a fighting art. It is not a competition. Have some fun too.