Only a few years ago I was also a first time student to yoga (I still remember my first class) and it was an exciting and slightly nerve-racking.
Once you have found a class that you want to go to and commit to a day there are a few things you can do to make sure you have a good experience.
Show up to class at least 15 minutes early so you can check in with the teacher and let them know it is your first class. The teacher will probably give you extra tips and help you out if you are looking around like you have no idea what you are doing.
Don't eat for at least 2 hours before class. That includes coffee but make sure you have plenty of water in you!
Bring water with you. Some linages of yoga don't suggest drinking water during class because the fire in your body works on digesting rather than the physical practice. But it's a good thing to have incase you start to feel dehydrated.
Figure out what mat you are going to use. If you have your own bring it to class. If you don't check with the teacher/gym/studio to see if they have mats you can borrow or rent.
Bring a towel. In some classes you are going to sweat and it's better to have a towel to wipe yourself down than to be sliding all over your mat. You can also place the towel over your eyes during savasana.
Wear clothes that you are comfortable in and can easily move around in. If you don't want your belly to show make sure your shirt won't slide up when you are upside down.
Be open to the new experience. Come to class with an open mind.
If you have any questions at all ask the teacher. They are there to help you with all aspects of the yoga class. They would prefer that you ask a ton of questions than have you not enjoy your first time in a yoga class.
Take a chance and see what your body can do! If you have any questions about coming to one of my classes let me know.