Civicontribute registration module with wordpress
Make sure you have enabled receipting in the Event configuration - and double check the to and bcc fields!

Reference: https://book.civicrm.org/user/current/events/creating-an-event/

Scroll down (lots) to Confirmation Email section.

If that's working: check that you can send Email from CiviCRM: go into your Administer -> System Settings -> Outbound Email -> and try send yourself a test Email;

Reference -> https://book.civicrm.org/user/current/advanced-configuration/email-system-configuration/