When you pay for your site you fill out an envelope you complete a receipt that lists the arrival/leave dates and then clip the tag to a post at the site. Rangers/hosts come around to verify payment/remove old tags. So if a site doesn't have a tag, it's open for the taking. If it's tagged and the date hasn't passed, it's reserved.

Once you get there and pick a site you do fill out a form and have it tagged to you.