Lisa,
If you are the administrator you should be able to remove the document. So if you click on Shared Documents on the left pane and it loads the shared documents page on the "main" page, and you point your mouse on the document under the column "name" it should markup the document name and you should se a little arrow to the right, clicking it should give you a dropdown list(click just outside the name of the document, otherwise it will try and open it) with some options and one of them should be Delete. Just make sure that you are not trying to do it from the Webpart on the mainpage, you have to do inside the Shared Document list.
If you still are not able to do that, check your userrights settings to really verify that you are an administrator.
Regards,
Thomas