Last year, my neighbor caught a caterpillar for us to raise until it became a monarch butterfly. I hadn't ever caught a caterpillar before, but she has done it every year since childhood. She just brought me the caterpillar in the jar. We enjoyed it so much I think we will make it our own tradition!
I figured someone on the Internet would have more experience and advice on the topic than myself, and I found it here: http://www.butterflyschool.org/teacher/raising.html
We broke some of the things listed on this site--like we obviously used a jar with a lid with holes in it (apparently a no-no), but our butterfly survived and thrived. You probably will want to ask around with people who live by you as to what type of caterpillars you can find, where to find them, and when. This site said most caterpillars pupate in the winter. Ours was late summer and turned into a beautiful butterfly late in September. So when this activity is right for you will depend on your climate and what types of butterflies you can find.
Raising a caterpillar into a butterfly is a lot of fun and a great science activity. You watch the caterpillar get bigger and bigger. Then you see it in its chrysalis. Then it comes out, you watch its wings grow stronger, you can hold the butterfly, and then when it is strong enough, you release it and watch it fly away!
Here is our butterfly exercising the wings: