There is a number of workflow questions around Composer that need official docs.
It needs to be made clear that Composer doesn’t need to be run on a server, it can be run locally and the resulting vendor/ directory committed/upload. Previous drush make workflows need to be mapped, etc.
Jeff Geerling's blog post is a good initial overview: https://www.jeffgeerling.com/blog/2017/composer-and-drupal-are-still-str..., we start from there. The next step would be to read the two drupal.org issues: #2845379: Provide optional composer integration but don't force users to understand how to use composer and #2477789: Use composer to build sites and extract their complaints.
Once posted here, these topics can be worked on.
Current documentation
This is a list of at least some of the places where we are providing Composer documentation already so that we can remember to read/update them.
- https://www.drupal.org/docs/user_guide/en/install-tools.html - Overview of what composer is, from the User Guide
- https://www.drupal.org/docs/user_guide/en/install-composer.html - Using Composer to download files, from the User Guide.
- https://www.drupal.org/docs/develop/using-composer - This guide contains various pages documenting using composer for various tasks and is likely the place that most people are going to find information