When you register for an event, you receive an automated email that has a subject starting with: "Registration Confirmation" - It'll then list the name of the race afterwards. Search your email for that. If you haven't received that email, it is likely you are not registered (or entered your email incorrectly).
Some races also have enabled the start list - they can list the people who have registered for the race. Check back on the registration page to see if that link is available to look up your name.
If you're still not sure, you can either contact firstname.lastname@example.org or the race director to have us help you.