Most vertebrates can be trained using very similar methods. "Stupid" animals like chickens and fish can actually be trained more easily than you might think, and the exact same techniques work on dogs, monkeys, and humans. My wife is training to be a dog trainer and we have trained guinea pigs, rats, cats, and dogs. That said, any attempt to "train" invertebrates has been a failure for us. I think the general consensus is that they are too stimulus and instinct driven rather than using more complex problem solving or memory.
Particular problems with training invertebrates include inability to communicate using signals (most vertebrates use audio-visual triggers for training) and troubles with reinforcing behavior. For example, how do you reward a mantis? Typical clicker training requires that the reinforcement be provided almost instantaneously to provide the best training. The lower the animals' intelligence, the faster you need to be or else they won't associate the reward with the behavior. Giving a fly to a mantis is not nearly fast enough.
I am not saying that training cannot be done, but I think the intelligence and lack of easy rewards makes most invertebrates impractical to train on even simple behavior. The next best thing is to give stimulus that feeds into the behavior you want. For instance, a puck light on the lid of the enclosure may provide a warm spot that the mantis likes. Since they like it, they will hang there more and therefore poop there more. Using this simplistic stimulus, you can guide the behavior you want, but I wouldn't count on them remembering the behavior when the stimulus is taken away.
If you want to work on training animals, I would start with Karen Pryor for information on effectively and humanely training animals. And if you like small animals, rats are a joy to keep and are one of the very easiest animals to train. They are by far my favorite caged pet.
And check out this short video showing results of chicken training:
https://www.youtube.com/watch?v=QLqsnavi-bY
