Click on your Inbox icon in your User Control Panel. A list of all your messages will appear.
Select the ones you want to delete by clicking on the little Mark square on the RHS of each message.
Go down to the bottom of the page and click on the menu box. This will say Mark/unmarked as important, which is the first option. You will then get an option to Delete Marked.
Of course you can also then go to your Sent box and do the same. Your account will only hold 50 of each sort of message, so if you go over this limit you won't be able to read any new messages.