I have someone who I have given full permissions to to make edits in one of my docs in a shared folder...how do they save those changes to the source document after they have downloaded and edited it?

The person must also has a DriveHQ account to edit / upload files in your shared folder. He/she must logon his own account, then access your shared files in the special virtual folder: "DriveHQ Share\YOUR_USERNAME\SHARE_NAME".

He can download the file, edit it and then upload the file back to the DriveHQ shared folder; 

The best method is to use DriveHQ FileManager. just double click on a remote file to open and edit it; when finished, just click on Save to save the file. It will be instantly saved in a local cache folder and then automatically sync-ed to DriveHQ online storage.

If the file is a Microsoft Office file, then you can also launch MS Office from Internet Explorer to directly edit a remote file.