Once a payment has been submitted for a participant, we don't let you delete them unless you refund all their payments. If they have not paid OR you have refunded them, go to their entry in Reports > Registrations. There will be a Delete icon next to their name.
If you have a participant whose payments are not being refunded and you want to treat them as deleted, you can remove them from their programs if you would like by going into the Programs menu, selecting them, and clicking on the Remove button.
Their profile will still be in the system, and you will see them if you go to Reports. But as far as communication goes, if you send to programs, they will not receive anything.
Finally, while you cannot delete a participant profile once there has been a payment for them, you can delete the actual user accounts associated to the participant. That way there is no way for them to log in, and they also will not receive any communication, even accidentally.
To delete the users, go to Security > Users and into their record. At the bottom of their details, you'll see a Delete button.