After the Vedic people moved into the Ganges valley about 800 BC, they were further from West Asia and Central Asia and had less contact with their relatives there. They mixed more with the Indian people. Indian gods mixed with the Indo-European gods and became Hinduism. The Mahabharata, first told about this time, tells the story of how the Vedic people took over the Ganges.
But still the Vedic people did not control all of India. In South India a bunch of kings stayed independent. They did not have to do what the Vedic people wanted. Stories of fights between the Vedic people and the southerners make up the Ramayana.
In the 500s BC, the Iranians under their kings Cyrus and Darius conquered part of north-western India (modern Pakistan). The Iranians were also Indo-Europeans, but they had left their homeland later and settled in modern Iran. The Iranians never really controlled India very well – they made the Indians pay tribute in gold to Iran, but the Iranians couldn’t really tell them what to do.
Meanwhile, the Vedic people continued to rule north-eastern India. Seeing how the Iranians formed a big empire, the Vedic people also began to put together bigger empires. As the Mahabharata says, this was a time “where big fishes ate little fishes.” with the big empires starting, big religions also began to form. Animal sacrifice began to seem old-fashioned. In the 400s BC, this was where Siddhartha Gautama, the Buddha, lived and started the faith of Buddhism. Jainism took off about this time too.
Learn by Doing – act out a scene from the Ramayana
Alexander the Great in India
More about Ancient India
Early India : From the Origins to AD 1300, by Romila Thapar (University of California Press 2004). For adults, and a little dry.
There’s also a good article on this, with some recent citations, on Wikipedia.