The belly talking technique, or stomach talking magic is ventriloquism, and yes, you'll really have to be on the lookout for a chance to use this word. Short of taking your Japanese friends to a hacky-comedy show, here's another way to use it:
I was having a conversation with a group of teachers, unaware that the vice principal was listening in. When he suddenly chimed in with his opinion, the teachers were caught off guard, and not quite sure where the voice had come from. They all started laughing about 腹話術, and then they had to stop and explain it to me.
Feel free to try this one whenever somebody pipes up out of nowhere (腹話術した), or if you want to tease somebody about being a parrot or a puppet (腹話術されている).