Unless you mean another type of authentication?
On the copy of MC that is acting as the server:
Options -> Media Network -> AuthenticationThen, on the client machines, make sure
Options -> Media Network -> Client Options -> Automatically Sync changes is enabled. The next time you connect from your client copies, they'll ask for the username and password you entered there on the server (there is a "remember this" checkbox though so no big deal).
The changes sync
periodically as MC is running (not instantaneously), or when you close the client copy of MC down. If you need it to happen immediately, you can manually initiate it from a client copy of MC by going to
File -> Library -> Sync changes with Library server (or just close out of MC).
Please note: While you can make tagging changes from a "client copy" of MC, there are some limitations on what changes you can make. For example, you cannot change Library Views in any way from a client copy of MC. It will let you do it, but the changes don't "stick" (they'll revert next time you connect to the server). Likewise, you can modify Playlists (and add new ones), but you cannot delete them. You can't rip CDs on a client either (though they've said this is something they plan to implement when possible).
Most of the restricted things are related to Library Views and importing new files.
PS. Why it works when you do it 2 or 3 times? It probably doesn't actually have anything to do with repeating the steps. It probably has more to do with timing. My guess is that it isn't actually "working" by syncing the database. Instead, when you tag the files, it is applying those tags to the actual files on disk (via the network share, likely), and then eventually Auto-Import on the server copy of MC sees these tag changes and updates the Library to reflect those changes.
Either that, or you do have the above options enabled and you weren't aware that the changes don't sync instantaneously.