In the spring we spread parsley seeds in a patch near the front door. We enjoy several months of herbal harvest until the caterpillars appear. Then we share the greenery, feeding our baby insects in their big jar.With parsley to eat and a stick to climb, they're happy campers.
Eventually they assume "the position", molt the final skin, and appear as chrysalises.We usually overwinter them in the fridge; mature butterflies emerge in the spring.
If you'd like to grow your own butterflies, try planting some parsley this spring. With some luck, a mama will lay her eggs in the summer and you'll have caterpillars to watch.
For more details, you can read my butterfly posts here (they're in reverse order, with the oldest at the bottom). Anna Comstock's Handbook of Nature Study has a lesson on Eastern black swallowtails, and Rick Mikula's The Family Butterfly Book is also a useful resource (I borrow it from the library).