To answer you question specifically to how Google Docs works. They use a technology called
Operational Transformation
You may be able to use one of operational transformation engines listed on: https://en.wikipedia.org/wiki/Operational_transform#OT_software
The basic idea is that every operation has a context, e.g. "delete the fourth word in the fifth paragraph" or "add an input box after the button". The clients all send each other operations thru the server. The clients and server each keep their own version of the document and apply operations as they come.
When operations have overlapping contexts, there are a bunch of rules that kick in to resolve conflicts. Like you can't modify something that's been deleted, so the delete must come last in a sequence of concurrent operations on that context.
It's possible that the various clients and server will get out of sync, so you need a secondary algorithm to maintain consistency. One way would be to reload the data from the server whenever a conflict is detected.
--This is an answer I got from a professor when I asked the same thing a couple of years ago.