| Are you taking or giving the lesson?
I have been teaching lessons at the local shop for about 4 years now and I know the feeling from the instructor's point of view. Even after all the time teaching, I still get first time jitters for new students.
If you are the student:
As Stacatto stated, most instructors use the first lesson to learn their student. I learn how experienced they are and how long they have been playing, as well as what genre of music they are interested in. Some people want to learn theory, while some people only want to learn others' songs. I usually do not charge for these lessons as a personal policy, but it depends on who you are learning from.
If you are an instructor:
My first student had been playing piano for about 30 years, so I was definitely nervous. He turned out to know little to nothing about the actual instrument, and was a great student when it came to applying theory. Though you may not ever get over the new student jitters, do not try to impress them right off the bat with big technical words. You can easily make them think you are snob-ish or (even worse) turn them off to learning music.
All in all, think of it as a new opportunity to make a new friend. As corny as it sounds, it is true. I keep up with several of my former and current students through email and phone. It really is a good way to make several musician friends. Another thing, and probably most important is the fact that the other person is just that; a person! They are probably nervous as well. It is almost like a job interview, but once you break that ice things should be smooth sailing.
I hope that helped at all, and good luck in your lessons!
-skabass13 | 
