Hey there! This is a complete, unofficial guide on the new Godot Asset Store. As it is in beta still, this guide will change. The current Asset Store actually does a pretty good job at explaining the fields so some of these notes are a little redundant.
I would also recommend checking out the older Asset Library's submission guide to see suggestions on how to layout your repositories and/or your asset zips.
When you are ready to begin, go log into the Godot Asset Store, or create a new account, then click the Upload Asset button at the top of the screen.