It actually seems to vary a lot between species and even individuals. Most people report that their mantis becomes skittish, stays upside down, refuses food, and in some cases, goes pale.
The only time my Hierodula membranacea has ever refused a meal is right after molting, when she gets oddly "picky" for some reason. She'll eat mere hours before molting (although feeding them at that time is NOT recommended and I don't do it deliberately) but she is still very adamant about being upside down and acts like I'm always trying to squish her at this time. I've also noticed her abdomen becomes dead weight prior to a molt; she'll drag it around and it will flop when she's upside down- and tilting her right side up results in highly alarming flailing motions.
As for what to do, remove all feeder insects, put the enclosure in a place where it won't be disturbed, and make sure the mantis has enough space and security to molt properly. Most people recommend bringing the humidity up slightly before a molt, but there is some disagreement about this. Personally, I've found extra humidity doesn't hurt.
Avoid handling the mantis until the new exoskeleton has hardened. How long this takes is dependent on species and environment, but a good rule of thumb is to wait at least 24 hours (preferably longer, if possible).