Does anyone know the process for gog games? For example once they get the ok from a publisher, does the publisher send them the game files or they get the games themselves,etc?

They generally keep it under wraps but we can make some assumptions:

1. they likely get the files from the publisher/dev
2a. patch to latest official patch if the files arent patched.
2b. compatibility work to make it run on modern systems
3. testing
4. wait for release.
5. release.