Visit your local library and check out Helen Gardner's classic reference book on art history, "Art through the Ages." Her book has long been a staple in art appreciation courses. Gardner devotes entire chapters to the art of Greece and Rome. Peruse the shelves for similar books; there are many with color plates that have chapters on Greek art. Begin with Greek art and work your way up to Roman art.
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Check out a copy of Edith Hamilton's "Mythology." Hamilton points out that the Greeks created the gods in the image of man rather than the other way around, as in Christian thought. Greek architecture, sculpture, and painting incorporated as its most prevalent subject matter the gods and goddesses and their stories, as well as the creation of the world and all things in it.
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Familiarize yourself with the first three chapters of Hamilton's "Mythology" to learn the most important myths as well as the gods and their character traits. You'll also learn the Roman names of the same gods and pave the way for your study of Roman art.
Examine photographs or plates of famous architecture, paintings, and sculpture honoring Greek gods. Learn to recognize Ionic, Corinthian, and Doric style columns and capitals to help establish various historic periods in your mind. Do this by looking at pictures and reading descriptions.
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View authentic art whenever and wherever you have access. Many cities have exhibits where genuine works by the masters are on display. No photograph can capture brush strokes, textures, or light and dark images like the real items.
Visit museums. Some are probably within driving distance of you. Even lesser-known artists dealt with the same subject matter as those famous artists. Figure out what gods you can identify, what story or event from Greek or Roman myths the painter is capturing.
Watch television documentaries and programs on art appreciation and art history. Many lectures and recorded programs are available for rent or purchase.
Check with nearby educational institutions to see if they offer classes. Go on field trips with them.
Go back to the library. Locate books on symbols in art. Painters worked them into their works. Aphrodite's tree was the myrtle. Athena's bird was the owl. The lyre belonged to Apollo, and his twin, Artemis, was the "lady of the silver bow." Learn to use symbolic clues in paintings and sculpture to help identify subject matter.
Read more about Roman art. You will phase into it during your Greek studies because the same gods appear in both cultures, albeit they go through changes, many subtle and others more pronounced.
Factor in Christianity as you begin to leave ancient worlds behind. More modern Greek and Roman artists took their stories and subject matter from the Bible and Christian works. Examine images of DaVinci's "The Last Supper" and Michelangelo's "David" and "Pieta."
Search online. Art websites abound. Universities embed links to sites across the Internet that are excellent resources for you to visit as you learn about Greek and Roman art.