On your event page you can link to your Facebook page.
This will create a 'Like' box and make it easy for people to like your brand.
When creating your event enter your Facebook page URL in the section named 'Marketing Information'
It must be a Facebook page - e.g. www.facebook.com/Freshtix
You can also add your Facebook event and allow people to RSVP on Facebook.
Please note: Your page must not have any age restrictions for this to work. If you apply age restrictions to your page only people logged in to Facebook who are old enough will be able to view your page and therefore the link will not work.
You'll find more information about Facebook's age restrictions here.