Native species and most of other species are approved by the USDA / APHIS and with no permits required. Always check your county ordinances regarding the more exotic species.
In any case, make sure you do your research. There are many sites out there that sell praying mantis eggs. Most of them have detailed instructions for the best results in egg-hatching as well as nymph feeding.
My brother successfully allowed two adult mantids to mate and the female ended up laying her eggs right in her cage. When the baby mantids finally hatched in the spring he put them in small separate vials and we took care of them the best way knew how.
At first we fed them fruit flies and when they got a little bigger, we started buying crickets from the pet store. Some of these adolescent mantids were able to tackle and devour crickets that were considerably larger than they were.
With each passing molt, the young mantids grew bigger and stronger. Some we were able to release in our backyard and some we kept for observation and study.
Before all this, we never even seen mantid nymphs. It was a wonder to watch them grow into adulthood.
By Noy Ilao