Read books about Roman art or art history in general. Art history books place each style and era into perspective with the eras surrounding it. A book specifically about Roman art will isolate the topic and give you a more in-depth understanding of the era. You will develop a firm grasp on the theme of the art by reading these illustration-rich books.
Learn about Roman art online. Many online resources allow the reader to learn about art from any culture and time period. Art.com provides a detailed account of the Roman art era, complete with links to images and book recommendations. Art-And-Archealogy.com details Roman painting styles complete with illustrations and descriptions.
Enroll in a college art history class. Take a general art history course to gain an in-depth understanding of not only Roman art but art history from other eras. Alternately, find a college that teaches a course about Roman art specifically. Enroll in Ancient Roman Art & Archaeology at New York University or Roman Art and Archaeology at the University of Washington.
Visit art museums in your area or beyond. Tour the the Greek and Roman galleries in the Metropolitan Museum of Art in New York City. Check out the Roman Art collection at The Museum of Fine Arts in Boston. This museum bills its Roman Art collection as "one of the best in the world." Most large metropolitan museums contain some sort of Roman collection from which you can learn. Search online for museums in your city.
Visit Rome, Italy. Tour the Vatican Museums to see extensive collections of Roman art. Visit the Sistine Chapel and marvel upon Michaelangelo's famous Sistine Ceiling. Visit the Borghese Museum, Galleria Colonna, the Capitolini Museum, Palazzo Barberini and various art-filled churches in the area.