Butterfly hunting is the most fun you can have killing butterflies with a gun. The objective is to take as much butterfly meat home to your family as possible for sustenance; without the precious butterfly meat your family will starve. It should also be noted that unless butterfly populations are kept low, the butterflies will undoubtedly attract hippies.
Most enthusiasts use an Ithaca Desert Weepinglotus with a 4.2mm. anus bleaching rounds. The rounds are armor piercing so as to thoroughly penetrate the butterfly's thin, fragile wings. Inadequate penetration may lead to disappointment.
The best thing to do is to dress up as a large flower and start photosynthesizing like crazy until the butterflies come.
In all states except liquid you must acquire an insect hunting license, which costs way more than you can afford. Also, don't hunt the endangered Manila butterfly unless you want trouble. Poachers of it have been severely mauled by it.
Type of butterfly
Ones which come close to you probably do not fear you. These make the best targets. Ones which are far away are hard to shoot so you shouldn't go after them.
Only point your gun at that which you intend to shoot. That being said, it is hunting etiquette to shoot everything you point your gun at it.