Sign up for a free Eventbrite account, or log in to your existing Eventbrite account and create an event. It’ll only take a few minutes.
Under Create Tickets, choose Free ticket. If you're collecting registrations rather than selling tickets, you can change the terminology on your event page to reflect this.
Once you've created your ticket type(s) and published your event, your attendees will be able to register for your event online. If you want to make changes or additions, you can always edit your event page, even after you've published it.