How do people put an image preview for the topic that doesn't show up anywhere in the thread?

He described it correctly. Click the Insert Hyperlink button (the little chain link) and put in your link, and it'll add the brackets and parens that tell the system to format it as a hyperlink using the text in brackets. If you leave those brackets empty, it puts nothing in the body of the text, and the link (if it is a picture) will show up as the image preview for the thread without being present in the post itself.

https://i.imgur.com/1HvNiEO.png?noredirect