Try to get there a little early. Sign the waiver and pay the monthly fee.
Go into the gender appropriate dressing room (we'll have to trust you on that) and put on your Dogi (uniform) or sweats. When you step onto the mat, bow.
Your first class will be a bit bewildering. Look around and follow the herd. If one person kneels down, maybe they are adjusting their gi; if everybody kneels down, you should too. If everyone kneels in a certain place, go kneel with them. In some dojo's, the seating is in rank order, so just go to the end of the row with the other white belts.
Generally, someone will be assigned to lead you through any warm-up exercises and will teach you the rudiments of falling. Someone else will work with you on the techniques.
You will be very goofy and confused. Welcome to my world; just enjoy the ride. Don't worry about doing it wrong, you'll be doing it wrong for some time. At the end of class, just follow the herd again. The bowing-out ceremony will be the same as the bowing-in ceremony. If you want to join in with the people cleaning the mat, ask how they do it. Every dojo does something different.
Now is a good time to ask any questions about aikido. You're officially an aikidoka!