You can use this module by importing it into your ~/.xmonad/xmonad.hs file:

 import XMonad.Layout.Reflect

and modifying your layoutHook as follows (for example):

 layoutHook = reflectHoriz $ Tall 1 (3/100) (1/2)  -- put master pane on the right

reflectHoriz and reflectVert can be applied to any sort of layout (including Mirrored layouts) and will simply flip the physical layout of the windows vertically or horizontally.

XMonad.Layout.MultiToggle transformers are also provided for toggling layouts between reflected/non-reflected with a keybinding. To use this feature, you will also need to import the MultiToggle module:

 import XMonad.Layout.MultiToggle

Next, add one or more toggles to your layout. For example, to allow separate toggling of both vertical and horizontal reflection:

 layoutHook = mkToggle (single REFLECTX) $
              mkToggle (single REFLECTY) $
                (tiled ||| Mirror tiled ||| ...) -- whatever layouts you use

Finally, add some keybindings to do the toggling, for example:

 , ((modMask x .|. controlMask, xK_x), sendMessage $ Toggle REFLECTX)
 , ((modMask x .|. controlMask, xK_y), sendMessage $ Toggle REFLECTY)