How do we know about Greek Mythology?
Although many stories were told orally in the beginning, there were great Greek writers who wrote down various versions of the stories in the form of poems, plays, legends etc. One famous writer was Homer who wrote the Odyssey and the Iliad. Another was Hesiod, the poet. The following sites are sources of some of the original writing.
Classical Myth : The Ancient Sources
The Perseus Digital Library

The Ancient Greeks also illustrated their art work with stories from their mythology. A lot of myths can be seen on their beautiful urns. Some good sites to explore mythology through art are:

Cleopatra Multimedia Guide to the Ancient World Art Institute of Chicago
Odyssey Online Michael C Carlos Museum
Looking at Art of Ancient Greece and Rome
Ancient Art - Detroit Museum of Art

Extension Exercise

Write your own myth and present it in one of the following forms:

As a child's reading book either on paper or as an electronic book using Powerpoint presentation or a series of Web pages or Shockwave director.
As a series of drawings to decorate a greek urn/s using paper or a drawing/graphics programme. The picture below is the shape that could wrap around the area near the neck of an urn.