it can't be done.
You can - and should! - use the regular back-up sync of your external hard-drive to back-up Zotero
http://www.zotero.org/support/zotero_data#how_do_i_back_up_my_zotero_library
but you cannot use Zotero's sync features with a local drive - to sync files you either need to use Zotero file storage or a WebDav server.
the webdav server can be installed wherever - there is, I believe, even a script for creating a webdav on your server somewhere on the forum.
Note, though, that the WebDav only syncs the files - the data would still sync with Zotero - free of charge regardless of size/volume.
The Zotero server code is available so, theoretically, the entire infrastructure can be hosted on an internal or third party server, but, to my knowledge, no one has done that yet.
Alex has started this here:
http://www.zitation.org/docs/start
though it never went very far - but that site also has links to the code and existing documentation by Zotero.
I don't understand the difference between files and data. The document 'sync' describes synchronisation of everything except attachment files. Does this mean that if a webdav server is created on a company network, only attachment files would be synchronised between a user and the server?
The sync doc page
http://www.zotero.org/support/sync
distinguishes between data syncing and file syncing.
data syncing is always with Zotero - it syncs the citation data as well as notes.
File syncing (i.e. the syncing of attachments) can be done with a WebDav or with Zotero File Storage, which is non-free over 100MB.
But even if you use the WebDav server, the data (i.e. everything but the attachements) will still sync with Zotero's Server. In fact, it's impossible to sync just the files/attachments.
OK, understood. Alternatively, is it possible to operate firefox (and zotero) on a network server and users would add citation references using the network installation?
dubious. How would you deal with several people trying to access Firefox simultaneously? And if you just put the FF profile on a network server you're going to corrupt the database in no time.
Upgrade Storage
You can - and should! - use the regular back-up sync of your external hard-drive to back-up Zotero
http://www.zotero.org/support/zotero_data#how_do_i_back_up_my_zotero_library
but you cannot use Zotero's sync features with a local drive - to sync files you either need to use Zotero file storage or a WebDav server.
Note, though, that the WebDav only syncs the files - the data would still sync with Zotero - free of charge regardless of size/volume.
The Zotero server code is available so, theoretically, the entire infrastructure can be hosted on an internal or third party server, but, to my knowledge, no one has done that yet.
Alex has started this here:
http://www.zitation.org/docs/start
though it never went very far - but that site also has links to the code and existing documentation by Zotero.
http://www.zotero.org/support/sync
distinguishes between data syncing and file syncing.
data syncing is always with Zotero - it syncs the citation data as well as notes.
File syncing (i.e. the syncing of attachments) can be done with a WebDav or with Zotero File Storage, which is non-free over 100MB.
But even if you use the WebDav server, the data (i.e. everything but the attachements) will still sync with Zotero's Server. In fact, it's impossible to sync just the files/attachments.
(that would require the setup I describe above - i.e. running the entire Zotero server structure locally).