Take a glass "core", run a 20- or 18-gauge wire through the top and twist into a little eyelet with a stem. Wrap some more wire around it for roughly triple-width neck, bring both ends of the wire together, and twist into a double-ply segment. Loop around several times to act as a framework, and you get this:
Next, take some 22-Gauge wire, anchor it by the middle to the joint at the eyelet-neck, and then go double-ply with it, wrapping it about the top to form the "cap" of the Gem. Instead of merely going over or under parts of the framework, fuse them into the weave, for a more uniform and less bulging/distorted look. You'll have something like this:
Next, got to the base of the framework, where the "cup" of the Gem would be, and begin weaving 22-gauge wire, like so:
Looks like a basket weave, right? Do this for the whole base, so you get something like this:
Finally, take a metal ring and "stitch" it into the base of the "cup" with more 22-gauge wire, so it can stand upright.
Now, the only thing left to do is make your Wish and focus on the Gem until you soul is inside...
(Green Gem prototype for current style used as an example - I have since cut and rebuilt the cap for it.)