If you want to find out the time that your user enrolled into an event, then first locate Manage Events under the Administration tab. Once you find the event that you want to manage, and then click its blue hyperlink.
Then locate and click on the second tab above, named Manage Enrollment.
Under this tab, you will see the date that the user was enrolled into the event.
Note: This information is only available up to 5 minutes before the event starts.