If you have not studied Greek mythology at all, I can see where it would be extremely difficult to understand the many allusions that poets, Shakespeare, and other well-known authors make to mythological characters and events.
When you read most classic works that contain mythological allusions, many readers or textbooks contain helpful footnotes which explain who the Greek person is or describe the event being referenced. If you do not have access to footnotes, of if you simply want to betterunderstandliterary works which contain these allusions, I would highly suggest reading Edith Hamilton's Mythology or perhaps obtaining a copy of Bulfinch's mythology "dictionary." Both works effectively break down the characters, stories, and vocabulary that comes from the myths, and most versions of Hamilton's book contain an index which makes it easier to find a specific character, creature, or reference.
One last note--once you know a little more about Greek mythology, try to connect why the author would make a reference in his or her writingto a specific Greek character or event; this type of analysis is what most professors what to see from their students, not a simply definition of the Greek figure/event, but rather,the "why" behind an author's alluding to him, her, or it. I hope that this helps!
I'll suggest some works you could read and study that contain mythological allusions:
- Shelley's Frankenstein, or the Modern Prometheus: read up on Prometheus and you'll catch the allusion.
- William Blake's "The Tyger" contains classical allusions. The enotes Study Guide on Songs of Innocence and Experience can help you identify the allusions.
- "Ode to a Nightingale" by John Keats makes heavy use of classical allusion. Any textbook that contains the poem should have notes.
- Other poems you could look at: Tennyson's "Ulysses"; "Ode on a Grecian Urn," by Keats; and Shelley's "Ozymandias."
Those should get you started.