I accidentally closed the introductory WriteMapper tutorial / guide. How do I open it up again?

You can do this from the menu bar of the app.

On desktop versions, simply navigate to Help → Open Tutorial WriteMap in the menu bar, while the WriteMapper app is open, and the tutorial will open once more in a new window or in your existing window, depending on if you already have content in your existing window.

For WriteMapper 2 on the iPad and iPhone, tap on the button that says "Open" in the first introductory screen that shows when you first access the WriteMapper app, and that should reveal a "Show Tutorial" option which you can tap to do just that.