It is very unlikely that you will come across butterfly eggs by chance because they are just too small. Therefore it is best to find butterfly eggs to hatch by finding a female butterfly in the process of laying eggs. You can tell when a female butterfly is about to lay her eggs when she is away from flowers, flying low over vegetation in a fluttery manner, and is repeatedly touching down or landing on various plants. When she touches down on the plant she may tap on the leaf with her front foot in a process called drumming to release chemicals so she can taste  the plant and identify it. Once on a suitable plant she will bend the tip of her abdomen down and deposit an egg on the top or bottom surface of the leaf. Most species of butterflies lay just one egg on each leaf, but a few species will lay 10 to 300 or more on the same leaf.  

Once you have obtained the eggs, you should put them in an environment where they can live. To do this, you should take a sprig of the plant that the eggs were found on and put its stem in water to keep it healthy. You should cover the container of water with something like cheese cloth so that the caterpillar will not fall into it and drown once it has hatched. The container that the caterpillar lives in needs to have 2 conditions met, humidity and temperature. Something like a small empty aquarium, a large plastic box or  a large glass jar with a wide mouth should work. The container should be covered with lots of tiny holes but there should not be a lid with holes poked into it. Poking holes in the lid and using it to cover the container will not allow the caterpillar to have enough oxygen and it may cause it to cut itself on the sharp edges of the lid. Sometimes you can find suitable containers like this at pet stores.

Caterpillars breath through tiny holes on the sides of their bodies called spiracles. If these holes dry out they can lose a lot of moisture or they could drown if they have too much moisture when the humidity is too high. To prevent them from drowning or drying out you should place a moist paper towel in the bottom of the container. You should also keep the container out of direct sunlight because it may warm the closed container so much that it hurts the caterpillar. On the other hand, if the container is too cool it may slow down the insect’s development.

When feeding the caterpillar you should be sure to give it the leaves of the plant on which you found it. If you know the species you can also look up what other plants it may eat. At first it will not eat very much, but as it grows, you may have to give it new leaves every day.

As time goes on caterpillar droppings will build up in the bottom of the container. You should clean these out regularly.

The caterpillar will also become still while molting. It is a good idea to have some twigs and sticks in the container for the caterpillar to crawl on when it is shedding or when it is looking for a place to pupate.

A pupae should be kept at an average outdoor temperature and humidity. When the adult emerges from the pupa it will hang upside down while its wings expand and harden. To do this it must have plenty of room. Otherwise, its wings may never fully expand and it won’t be able to fly. Therefore, pupa should be kept in a large container where there is a way for the butterfly to crawl up on a branch or screen and hang upside down. This container should not be a glass jar because it is difficult to climb up the sides of a glass jar.

Once the adult’s wings have hardened, you can carry it outside in the container and place the opened container near flowers so that the butterfly can leave and feed. Keep in mind that, once your butterfly has emerged, some butterflies only live for a few days, so you would need to release it quickly if you are going to let it go.

When you collect the eggs it is important that you know about the butterfly’s overwintering stage. Because of the butterfly’s overwintering stage, you may end up with an egg that doesn’t hatch, a pupa that does not open, or a caterpillar that stops eating before it is full grown and starts wandering about. When these things happen it is a sign that nothing more will happen until spring, but you must provide your pet with the right conditions for overwintering. When an egg, pupa, or caterpillar are in the overwintering stage, they should be placed outdoors and away from direct sunlight. If it is a caterpillar, you may provide it with some dry leaves and a little bark. Once spring comes, you can bring it back inside and it will continue its development.

The overwintering form of a species can be found in many places including field guides and websites such as Butterflies and Moths of North America (http://www.butterfliesandmoths.org/) and The Lepidopterists’ Society (https://www.lepsoc.org)