There is no “right way” to document your ecosystem. The process is usually a dance between capturing the detail in an orderly way and then realizing that the detail is holding you back. Time to throw it away and break through.
Capturing in an orderly way means that you’ll need some drawing software or something like mindmapping software for capturing “connections” or “flows”.
Breaking through ( and starting ) usually requires a whiteboard ( or napkin ). Often “post it notes” help because they make it less official and one is willing to be more free. “Post Its” because some people can’t even put stuff on a whiteboard because they believe they are committed to the idea.
Here are some links to people who are good at sketching and some Mind mapping software.