Sorry to hear you had trouble figuring it out. Did you go through the screenshots at all? They give you an overview of Tab Stash's functionality.

Tab Stash saves its bookmarks (= stashed tabs) under a special "Tab Stash" folder in "Other Bookmarks". "Stashing" a tab means saving its URL as a bookmark and hiding the tab but keeping it open in the background. If you close the browser window, the tab is closed, but the URL can be revisited again by restoring it from your stash or opening it directly from your Firefox bookmarks.

Multiple browser windows are not a problem—they are treated separately. Each has its own list of Unstashed Tabs / Open Tabs.