Can you see the tiny caterpillar next to the hole in the leaf? It is only a millimeter or so long. And very well camouflaged! Exactly the same color as the leaf. This is a Cabbage White on Nasturtium.
I like rearing them because they are easy to find and easy to rear. They can be found across the US wherever cabbages or nasturtiums grow. The larvae (caterpillars) can be hard to find because they are the same color as the leaf. The eggs are easier because they are white.
When rearing, I usually like to start with an egg, because I like to see all the stages. Also, if you have time to sit in the garden waiting for a female to lay eggs, they can be easy to find. At any rate, finding the critter is the hard part, everything after that is easy.
The caterpillars usually stay on the food plant when young, so a cage isn't really needed until later. The sometimes leave the plant to molt to a larger instar. They usually leave the plant when ready to become a chrysalis. That is called "wandering." So a cage is a good idea when they get big. You can read about homemade cages in my "Caterpillar Cages" blog post. It was my first!
Once you find an egg or caterpillar, decide if you want to rear it inside or outside. If you rear outside, you can put a net sleeve over the plant. Make you you check frequently, because sometimes the critters eat all the foliage inside the sleeve.
If you want to rear inside, get a vase and fill it water. Then cut the branch of the plant with the critter and put it in water. The leaves provide both food and water, so it must stay fresh.
Then you can watch it grow. After a few days, the plant will start to fade. For tiny caterpillars, you can use a watercolor brush to transfer them to a new leaf. Older caterpillars you can gently pick up. But don't handle them too much! New research indicates that it is really stressful.
When they are young, you can just put the vase on a piece of paper on a table. The frass (poop) will fall on the paper, and it is easy to dispose of. When they get older, put them in a cage. A net cage is best. They will pupate on the netting, or on sticks that you provide.
The length of pupation can vary from a few days to a few years. Crazy, huh!? Some butterflies overwinter as pupae. They may emerge the next spring, or they may wait until another spring. Emergence seems to be better is they experience a real winter, so put them someplace unheated like a garage or basement in December and January. Don't forget them! Put them back in the house in February so that you will notice when they emerge.
After the adult butterfly emerges from the chrysalis, It is best to give it 2-24 hours to expand its wings. Then release it outside on a sunny afternoon. Butterflies make the best pets because you never see them die. You just watch them fly away into a beautiful blue sky!