Events can be organized into different calendars. You can specify multiple times and even limit the number of people who can sign up for each time along with enforcing a registration deadline. You can use the built in sign up form or design your own including the option to require payment during registration.
These events can be shown on the calendar for other guests to view and sign up for. They can also be embedded on your church web site for a more branded experience.
You can track attendance at an event using the check-in system as well (such as for worship services).
Learn more about how to add events and manage the different calendars.