You should definitely go! It will mean a lot to your friend :)
The Bat Mitzvah marks the transition from childhood to adulthood, and it is a very important day for Jewish people. Boys always have one, and often girls do as well. Your friend will stand at the front of the synagogue and read a portion of Hebrew; I'm guessing she must have been studying quite hard for it!
Then there will be a kiddush; wine, cakes and sandwiches, usually.
I think you should tell your friend that you'd like to know what to expect; it's a totally reasonable request!
I would suggest you just watch everyone else; they will say brief blessings/prayers before drinking wine and eating the food. Find out if your friend belongs to an Orthodox or Reform/Progressive synagogue - the latter are more relaxed.
Try this site, you'll find it helpful:
http://www.jewfaq.org
Also
http://askmoses.com
Have a wonderful time!