How do you hang stained glass without a frame?

I would definitely make a frame so its secure first before trying to hang it.

http://everythingstainedglass.com/tag/framing-hanging

The glass bits around the edge are not fully encapsulated without a frame. This is a risk -- damage and / or injury. I would recommend taking them to a picture-framing business and seeing if you can't get a reasonably cheap metal frame cut to size.

My client had small stained glass art pieces that had soldered rings on the top, and I simply took tiny screw eyes and screwed them into the wooden window frame, and then got some thick clear fishing line and tied it off on the glass piece's ring (I did burn the knot with a cigarette lighter ever so quick to melt the line, practice on some before you try on your piece) and then run the line and hold the glass to the height you want and tie off after knotting on the window frame screw eye.

If the piece is larger, I have used fine chain you can get at the hardware store, and use a tiny cup hook in the window frame.

You could use a plate hanger, maybe. But I agree that a frame would be more ideal.

I put two 24" x 30" antique leaded and stained glass windows over my existing windows by using mirror clips. I just screwed the clips into the existing window frame three per side. They hung on my windows without incident for 34 years. So easy to remove to clean both sides and then put back up, and cheap to boot. Just moved into a new house with no windows to hang the stained glass over so am researching how to frame them as standing pieces. No luck so far!