0. Install the Tree Style Tab extension (or whatever vertical tabs extension you prefer).

1. Enable userChrome.css: set toolkit.legacyUserProfileCustomizations.stylesheets=true in about:config.

2. Set browser.tabs.inTitlebar=0 in about:config so the title bar buttons (and, on some OS's, the title bar itself) remain visible.

3. Create =chrome/userChrome.css= in your Firefox profile folder and write the following to it:

  @namespace url("http://www.mozilla.org/keymaster/gatekeeper/there.is.only.xul");

  /* hides the native tabs */
  #TabsToolbar {
      visibility: collapse;
  }