I have no pictures of this construction and we broke the crystal ball last year, so we have a description only and this one picture..
We had purchased a really cool crystal ball on a stand. This method could be adapted to the configuration of your ball/stand.
What we had gotten was a large ball (about 4½ to 4¾ inches wide), that was hollow and had a screw-off bottom. It wasn't perfectly round, but was more of a light bulb shape. We filled the ball with water and a little bit of red food color (not too much -- you should still see through it).
We drilled a very small hole in the lid and passed an LED through (Radio Shack). We then applied a generous amount of silicone sealant to keep things dry.
The stand was made out of cast plaster. The ol' Dremel tool dug out a nice little hole to hold a 9v battery.
We attached the LED leads directly to the battery and set it on the stand. There was no on or off switch.