Acquaint yourself with the fantastic, non-sequitur images of works by Man Ray, Salvador Dali, Rene Magritte and others. Arguably, Magritte's most famous painting "The Son of Man" features a man in a bowler hat with a green apple obscuring his face. Surrealist art plays with subject matter, images and form, and leaves the viewer wondering "What does it mean?"
Visit your local museum. The Los Angeles County Museum of Art (LACMA), the Metropolitan Museum of Art in New York and Chicago's Art Institute feature surrealist paintings by Magritte, Dali and others in their permanent collections, and often feature special exhibition by other surrealists. Even small town galleries feature surrealist work by local artists.
Study surrealism by attending a class at your local college or museum. Many schools offer non-credit art appreciation courses in their adult education programs. Museums and art galleries sometime have free or low-cost seminars where students can learn about techniques and history behind the artwork they admire.
Progress to the appreciation of surrealistic art films. Famous movies such as Alejandro Jodorowsky's "El Topo" and Maya Deren's short film "Meshes of the Afternoon" included seemingly unrelated images and situations that intrigue and frighten movie-goers and make them think.
Try your hand at surreal art. Get colored pencils, watercolor and artist paper and improvise, or simply sketch stream of consciousness images on a pad of paper. It doesn't matter if the images "make sense." Surrealism is about self-expression and emotion.