Identify the type of hair growing on the caterpillar. Some caterpillars have hair all over their bodies, while others simply have tufts of red hair. Some caterpillars may have hair that looks more like spikes or spines.
Look at the size of the caterpillar. Certain species of moths and butterflies have different sized bodies. Use a ruler to measure the length of the body, but don't touch the caterpillar, as some fuzzy caterpillars sting.
Look for other colors on the caterpillar. The woolly bear caterpillar, which grows into a tiger moth as an adult, has a red body with two black ends. The bihar hairy caterpillar has red and yellow hairs on its body.
Use these defining characteristics to find the type of caterpillar in a book or online. In the United States, there are just a couple of red fuzzy caterpillars. The main two are the woolly bear and bihar hairy caterpillar.
Take the caterpillar to the local horticultural extension office for identification if you cannot find the type of caterpillar online or in any books.