The earliest buildings anyone knows of from India are from Mehrgahr, from about 7000 BC. But the first real stone architecture dates to about 2500 BC, in the Harappan period in northern India (modern Pakistan). The Harappans built big cities, with walls around them and public baths and warehouses and paved streets. But when Harappan civilization collapsed, about 2000 BC, almost two thousand years went by before anybody in India built a big stone building again.
When Indian architects did begin to build big buildings again, about 250 BC, at first they built them of wood. Nobody in India knew how to build big stone buildings so they wouldn’t fall down. Architects started by building solid stone buildings, basically mounds of dirt covered with brick or stone like the earlier ziggurats in West Asia and the pyramids in Egypt or Peru. People called these buildings stupas.
Soon after this, about 200 BC, architects began to carve Buddhist temples into the sides of cliffs, so they were taking away stone instead of building with stone. This is easier, so it was a good place to start. But under the Guptan Empire, about 350 AD, Indian architects finally began to build stone temples. These were mainly Hindu temples. Between 350 and 1000 AD, architects built better and better stone temples, especially in southern India, while in northern India they kept on cutting more temples into the side of cliffs, at Ellora and Elephanta.
Slowly Indian architects got better at building temples. Around 500 AD, architects began to use mortar to hold the stones together. Temples got columns around them, and towers over them. About 1000 AD, Indian architects began to replace wood beams with iron beams.
When Abbasid invaders came to India about 1100 AD, most people in northern India converted to Islam, so Indian architects built a lot of Islamic mosques, often re-using pieces of destroyed Hindu temples to show that they had defeated Hinduism. But in southern India, people went right on building bigger Hindu temples with fancier sculptures carved on them.
Learn by doing: build a city out of wooden blocks
More about Indian Architecture (the Harappan period)