As a counseling patient and as a Resident in Counseling I have experienced that many people are unsure of what to expect at their first appointment. This can add even more anxiety to the situation, which you probably had to work up some courage just to get yourself into!
To me, the most important thing about starting counseling is to do only what feel comfortable to you. Answer only the questions you feel comfortable with answering, and ask all the questions that come to your mind. Try not to worry about sounding silly, or doing something wrong. Clear up anything that is "gray" or unclear to you because the base component of a helpful therapy is trust and openness.
This article does a nice quick job of summing things up for any therapy newbies. Just remember that all counselors have differences in style, method, and approach, so no one first session will be exactly the same. You can also search "your first therapy appointment" to find even more useful articles written from different perspectives (thanks google!).
-Emily Bura, MSEd, Resident in Counseling