I have this lead light mirror, how would I go about wall mounting it? It presently has no backing of any sort.
For a "floating" appearance you could use construction adhesive (or "mirror adhesive") to mount a board to the back of the mirror (just the central mirrored part), and use some form of hanger or French cleat to attach that to the wall, with the mirror itself out a bit from the wall.
That would lend itself to wrapping that board with flexible light strip or rope lights to "halo" the mirror a bit and emphasize the stained glass edges by lighting behind them.
Use mirror clips, and plenty of them.
If you don't want to use hollow wall anchors, you might want to build a wooden frame as an attachment point for the clips, and then you can put them wherever the mirror needs them.