Obtain a good field guide with colour illustrations or photos from your local library, bookstore or nature centre.
Go on the Internet which features many good sites, such as Iowa State University's Bug Guide or Discover Life. Some sites even allow you to upload your own personal images of caterpillars you want identified and experts will get back to you with the specific species.
Identify caterpillars by visual features including main body colour, body pattern, hair density or tufts, and distinct features, such as tails (which are sometimes split), horns, knobs, lashes and spines. By identifying these features, you can easily hone in on their identities.
Identify caterpillars beyond just the visual elements. Caterpillars can also be identified by knowing body length, the type of plant they feed on and the location where found.
You can obtain free or low cost field guides with colour illustrations or photos at local nature centres, agricultural extension offices and state natural resources and wildlife departments.
Caterpillars can be noxious (poisonous) particularly if barbed, spiked or tufted. They are also fragile and can be injured easily. Limiting the handling of caterpillars for identification purposes will alleviate the problem.