Teenie tiny clothespins, jump rings, beading wire (20 gauge), needle-nose pliers for jewelry, and wire cutters.
I used an existing charm to measure how big I wanted the rings to be. Snip a piece of the wire for that. Make sure to add about half an inch to the length so you can loop both ends closed with the pliers at the end. I think this ended up being about 2.5-3 inches (you can always trim later). Then cut a small piece to make another jump ring. I think mine was a little less than an inch.
Next slip the small piece of wire through the clothespin and put the jump ring on. Then use the pliers to bend the small piece into a ring. Now you should have a little two link chain from the clip.
Thread the 3 inch wire through the jump ring and bend into a nice circle. Use the pliers to bend the two ends into tiny circles as well to finish those off.
Now you have a customizable wine charm or glass marker or whatever you want to call it.