To play Neverwinter Nights online, you will require a unique CD key. You can find it in your Account on the website: https://www.gog.com/account (not yet in Galaxy), under MORE -> SERIAL KEYS. Please input it in the Multiplayer Key Changer that you can find in the Start menu, or in Galaxy, under MORE -> Other -> CDKey Changer.
Changing the CD key will result in the premium modules (like Kingmaker) not working anymore, because they will use the default key for validation. To get around this, go to your My Account page and find the "premium modules re-installer", under the game's additional content. Download this file and install it. The modules will now be adapted to the new CD keys.
Please note that Neverwinter Nights 1 and 2 master servers are no longer functional. You should use the Direct Connect option to log onto your preferred server via IP address.
The current list of active servers can be found here: http://yourserverlist.com/