1)Look to your upper left and click on UserCP
2) Under Your Control Panel, there is a link Private Messages.
3) If you want to delete a whole folder (inbox or outbox), click on edit messages.
4) Click on empty folder(s)
5) If you want to manually delete posts, go back to Private Messages and click on List Messages. It's defaulted to the Inbox but you can change the view to Sent by using the pulldown on top of "Private Messages in Folder: Inbox to Sent items"
6) Here you can check them individually and then delete them by the pull-down at the bottom of the page, select delete and press the Go button.
7) Rinse and repeat.