The Bead Monkey and then found this excellent tutorial video online. So if you want a video version of this, click that link! If you prefer photos and text, read on!
The Basic Idea: Each cage is made with 4 jump rings which are joined to make sort of a tiny box for a 'captured' bead, which is not connected to anything.
The hardest part is finding the right size jump rings so that they fit around the bead, but are not so loose that the bead falls out. I used 8mm beads and 11.5mm jump rings, and they were just a hair larger than I would have liked. They worked well as long as the jump rings were perfectly tightened, but if they were loose at all the beads sometimes slipped out.
Of course you can experiment with different types of beads and different color jump rings to get a wide variety of results!
How to make the cages:
1) Start with two small connecting jump rings.
2) Loop two of your large jump rings ('A' rings) through these two small jump rings
3) Loop two more large jump rings ('B' rings) through the 'A' rings
7) Thread two new 'A' jump rings through the top of both 'B' rings, one on either side of the bead. Notice how the new 'A' rings sit INSIDE the ends of the previous 'A' rings.
This is how the jump rings fit together as you add more cages (again, notice how the ends of one cage fit inside the previous one):
After you have made your last cage, use two more smaller connecting rings to 'close' the chain. This is how the caged bead chains attach to the regular chain:
As I mentioned before, the hardest part is finding jump rings and beads that are 'just right' sizes for each other. If the bead is falling out easily you need a larger bead or a smaller jump ring. In general it seems that the jump rings should be just a little larger than the beads. Thicker jump rings will need smaller beads. If you know a formula for determining bead/jump ring size please let me know!
If you make the entire necklace and everything seems to be going well then suddenly one of the beads falls out it may be that those jump rings weren't quite tight enough. Sometimes I will over-tighten jump rings if a bead keeps falling out and I don't want to get a larger bead.