How is a paper with multiple authors usually written?
I think that this article from the Research Whisperer covers aspects of how multiple authors can collaborate to get a paper done. It is an interesting and quite brief read that I would recommend. 

TL;DR version: 


One leads the project and the initial drafting with others
contributing to an almost complete draft. 
The team splits the work into broad sections for each collaborator, which then draft, combine and revise.
Decide on all the details and each writes its own section with minor final corrections. 


From my experience, the first one would be the most common with an almost final version making it to the very senior people in the article.