Hi again. Please forgive the lack of built-in uploading in the plugin. That's a function I hope to add but the plugin is growing with my programming experience. (Read: I don't know how to do that yet, haha.)
You can upload using WordPress's built-in facility, or via FTP to your web site. In the case of the former, you can use the "Add Media" button above the editor (looks kind of like a star). Once the document is uploaded, get the URL of it and use it in the GDE shortcode (paste it into the URL box if you're using the new editor button).
Using FTP you can manually put the file anywhere you want on your web site, ie., create a folder for such documents etc.
Hope this helps.