If you need to completely delete a recipient record and all of it's associated data:
First of all you should search for the recipient to open the Recipient View.
Once on this page there is a Delete Recipient button in the bottom right corner.
Deleting a Recipient will irrecoverably remove their email address, profile data and list assignments and any message activity related to this recipient will be permanently anonymised.
For this reason you are advised to only do this if you are completely sure you wish to delete them from your database.
It might be that you simply want to remove them from a list.