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 began to mix more with the Indian people and the Indian gods became mixed with the Indo-European gods. The Vedic conquest of the Ganges is remembered in the Mahabharata, first told about this time.
But still the Vedic people did not control all of India. In South India a bunch of kings stayed independent and did not have to do what the Vedic people wanted. Stories of fights between the Vedic people and the southerners are told in the Ramayana.
In the 500s BC, part of north-western India (modern Pakistan) was conquered by the Persians under their kings Cyrus and Darius. The Persians were also Indo-Europeans, but they had left their homeland later and settled in modern Iran. The Persians never really controlled India very well - they made the Indians pay tribute in gold to Persia, but the Persians couldn't really tell them what to do.
Meanwhile, the Vedic people continued to rule north-eastern India. Seeing how the Persians 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.