I have always connected with MySQL Workbench to the databases of my Trellis projects.
In the current documentation it only shows how to connect with trellis-cli with certain applications.
Where can I see the settings needed to manually connect to other database management applications? (especially for development environment)
Primarily I access the databases using WP CLI (with WP CLI config file).
By default the database server on Trellis is not accessible from the outside (except you are using an external database server).
You can set up a SSH tunnel or expose the database server - but then ensure it is properly secured.
Related discussion:
I just re-added the connection details to the docs:
https://roots.io/trellis/docs/database-access/
Thanks for the topic 
Great, thank you very much!