You must have an account level of "Administrator" to be able to delete projects.  Here are the steps to deleting a project:

1. After logging into the authoring tool, you will click on the "Admin" tab.
2. Look for the heading "Projects" and click on the link "View/Update Projects." 
3. You will see a list of all your projects.  Locate the name of the project you want to delete.  Click on the "delete project" link to the left of the project name.  
4. You will see a pop-up box that asks if you are sure you want to delete the project.  Click "OK." 

Warning:  Deleting projects cannot be undone. If you delete a project you will not be able to revert to previously saved backups. The project will be unrecoverable.

An alternative to deleting a project would be to archive it.  Read this blog post to learn more about how to archive projects.