As I recall from ones I've seen, the ball is filled with sphagnum moss and as the plants are added, more is packed in around the roots, so they're held securely in place.
You can also buy sphagnum moss in sheets. Or you could use a mat of coir, i.e. shredded coconut fiber. These products are often used to line hanging wire baskets, so the soil doesn't fall out. You could line the ball with something that, then pack the center area full of moss, or even cactus/succulent mix, depending on the kinds of plants you're using. Cut x-shaped openings in the sheet moss or coir matting, so you can insert the plants. Then pin them in firmly and pack some additional moss around the roots to secure them and kind of hide the pins.
They're very pretty. Why don't you post some pictures for us when your done? I would enjoy seeing them.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams