The Bat mitzvah will have a service where the Bar Mitzvah child leads the service in some combination of Hebrew and English. This is a major accomplishment and one they have prepared for over a year. To attend the service, dress conservatively like one would for any religion. Girls keep shoulders covered. Boys wear a suit and tie or khakis/blazer. Those services are open to the public, so you may attend if you are interested too. Following services, there is usually a little snack - think juice and cookies, but sometimes lunch.
After the service that day or evening, there is a party to celebrate. Some are simple some are extravagant. Kids usually wear the same dress from the service, often with sneakers instead of dress shoes. This party is by invitation only, so plan to drop off and pick up.
The hosts usually have someone chaperone the pick up, especially if late at night.