You can catch and study the butterflies fairly easily. All you need is an empty jar(s) and a net. Jars can be made with Iron, Gold, Lapis/iron, Emerald/iron, or Diamond. And they range from easiest to break to longest lasting in that order.
The butterflies won’t despawn so you can keep them alive without worrying if they’ll disappear when you leave the game and come back. Once you’ve created a habitat, you simply need to right-click your full jar on the ground to release the butterfly.
Alternatively you can pin dead ones up in frames to hang them on your wall.
This mod also comes with a craftable encyclopedia that contains important information on the butterflies you catch. The information is based off of actual butterfly entomology so you can really learn a lot from this mod too! Rare butterflies can even be traded with Villagers for diamonds.