The I Ching Oracle is quite simple, although its interpretation can have many nuances and requires some understanding of ancient chinese symbolology. Traditionally, a fortune teller would cast coins, or yarrow stalks several times, generating a hexagram.
A hexagram is made up of six lines, which are either solid (yang) or broken (yin). These combine into two trigrams, one on top of the other. Each trigram represents an elemental principle: Earth, Mountain, Water, Wind, Thunder, Fire, Lake, and Heaven.
The two trigrams together, one on top of the other, represent an archetypical situation, based on the interaction of the two principles involved.
In addition to being broken or solid, each line of the hexagram is either "old" (ready to change into its opposite), or "young" (unchanging). This results in a second trigram, once you figure out what the lines will be after any changes.
So a toss of the coins represents 64 initial situations, with stable and unstable elements, changing into 64 possible secondary situations.
Wikipedia has a nice succinct (as these things go) explaination. For a more thorough study, and one of the nicest published editions, I recommend the Wilhlem/Baynes translation.