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There are 20,000 species of butterflies on the planet, with over 725 different species in North America alone. Before going out to look for caterpillars, you may want to do some research about which caterpillars are native to the area that you live. You can often find a list of native caterpillar or butterfly species on your state's official website. Try asking the librarian at your local library to help you locate books and periodicals that can help you identify native caterpillars in your area. You can find a list of state wildlife websites to help you find caterpillars here: https://www.fws.gov/offices/statelinks.html Once you have identified the types of caterpillars in your region, you can narrow down your search by what kind of caterpillar you'd like to have for a pet. Different kinds of caterpillars develop into different kinds of moths and butterflies, so you may choose one based on its caterpillar state, or on what type of butterfly you'd like to see emerge from the cocoon. Some caterpillars can be dangerous to touch. You may want to take that into account when choosing a type of caterpillar to start looking for. You may want to choose a species of caterpillar that you have ready access to a food source for. Caterpillars prefer leaves from their "host plant" to eat. Different kinds of caterpillars (and therefore butterflies) prefer to reside in different kinds of plants, so It's important that you choose what kind of caterpillar you're looking for in order to know where to look. The plant a breed of butterfly prefers is called a "host plant." Some examples of host plants for certain species of caterpillar are: Monarch butterfly caterpillars prefer milkweed plants. Spicebush Swallowtail caterpillars tend to reside in spicebush. Your best bet to find a Zebra Swallowtail caterpillar is in a Paw-Paw plant. Black Swallowtail caterpillars are commonly found in parsley, dill, or fennel plants. Luna moth caterpillars can be found in both walnut and sweet gum plants. Cecropia Moth, Viceroy or Red-Spotted Purple moth caterpillars can be found in cherry trees. Different caterpillars are more active at different points of the year, but nearly all caterpillars can be found in the Spring and Summer months. You will likely not be able to find caterpillars beyond the early stages of fall. Some caterpillars enter a state similar to hibernation throughout the colder months. Other caterpillars lay eggs that stay dormant until spring. It may not be easy to spot a caterpillar right away. Caterpillars often blend in with their environment as a defense mechanism against predators. One way to spot a plant that likely has caterpillars in it is to look for signs that a caterpillar has been feeding on a plant recently. Different kinds of caterpillars will leave different eating damage, so it's important to look for the type of damage caused by the caterpillar you're looking for. You can find photographic examples of different caterpillar eating damage here: http://www.raisingbutterflies.org/finding-immatures/caterpillar-strip-patterns/ Caterpillars cling tightly to the leaves and branches they are on, so pulling on it could injure the caterpillar or even pull off its legs. Instead, place your hand, a leaf or twig in the path of the caterpillar and allow it to crawl onto it to transport them. Be careful not to touch fuzzy or spiny looking caterpillars, as the bristles you see may be a defense mechanism that can cause skin irritation. Always wash your hands after handling caterpillars.

Summary:
Find out which caterpillars are native to your region. Determine which kind of caterpillar you're looking for. Research the plants in your yard or area. Start your search in the spring. Look for caterpillar eating damage. Catch a caterpillar by letting it come to you.