This guide will assist you in deleting messages:
Deleting a message is very simple, first check the box next to the message you'd like to delete, then select "Delete" from the Delete drop down menu:
This action will move the message into the Deleted Items folder.
To fully delete the message, navigate to the Deleted Items folder, and repeat the process from before:
Making sure that this process is done frequently and correctly will ensure that you do not hit the space limit on your account.