There is a different process for deleting a participant from a campaign, depending on the type of participant they are.
Delete a Donor
To delete a donor, you will first need to delete and refund their donation record from the admin (see here for a how-to). Once that's done, locate the desired participant under People > Contacts, and click "Delete" in the top left corner.
Delete a Registrant
If the registrant is also a donor, the donation must be deleted and refunded before they can be deleted; see above.
Otherwise, locate the desired registrant under People > Registrants, and click "Delete" in the top right corner of the registrant window. Please note: when double-clicking a registrant, you may need to scroll right to reveal the "Delete" button in the ensuing window.