Books
The main sources I have used for the history of ancient and medieval India are:
Thapar, R., The Penguin History of Early India, Penguin, 2002, is a full and scholarly overview of the subject, from origins up to 1300 AD, for the general reader.
Keay, J., A History of India, Harper Collins, 2000, is an accessible introduction to Indian history.
Auboyer, J., Daily Life in Ancient India, Phoenix, 1965, is a highly readable look at life in ancient and early medieval India from 200 BC to 700 AD.
Schmidt, K.J., An Atlas and Survey of South Asian History, Sharpe, 1995, provides a clear map-based approach to Indian history, invaluable for the Western reader who is unclear on Indian geography.
A lavishly illustrated work on archaeology for the general reader which includes good coverage of ancient India and the roots of Indian civilization, is Renfrew, C. (ed.), Past Worlds: The Times Atlas of Archaeology, Times Books, 1995, p. 88-9; 130-1; 188-9.
A work on general archaeology aimed more at students, but readable and with very good coverage of ancient India, is Scarre, C. (ed.), The Human Past, Thames & Hudson, 2005, p. 518ff.
Websites:
The British Museum’s beautiful series on ancient civilizations includes their website Ancient India.
Wikipedia has its usual vast amount of information on the History of India – but bee aware, it’s very patchy. Some of the contributors seem to have a hazy understanding of the difference between mythology and history.
The Ancient History Encyclopedia has a good section on the Indus Valley – Ancient India – but is a bit sketchy on the rest of ancient Indian history.