The first people seem to have reached India from Africa around 40,000 BC. At first they were hunters and gatherers, like other people around the world at this time. But by around 4000 BC, these people had begun farming and by 2500 BC settled in the Indus river valley, where they began to live in cities and use irrigation to water their fields. This is a little later than in West Asia, probably because India was not as crowded as West Asia at this time. A lot of people think that the reason they began to farm, and then build cities was that a gradual warming trend was making it harder to get water, and harder to find wild plants to eat, every year. So every year more and more people moved into the Indus river valley, where there was still plenty of water. When it got really crowded there, people began to build cities.
There were two main cities that we know of, Harappa and Mohenjo-Daro, about 400 kilometers (250 miles) away. Both are in modern Pakistan. The people of these cities lived in stone houses two and three stories high, and had sewage systems. They used bronze tools. They may have learned to make bronze from the Sumerians.
The Harappa people used an early form of writing based on hieroglyphs, like the Egyptians. But we can't read it, because there isn't very much left of it.
By around 2000 BC, though, the Harappan civilization had collapsed. We don't know what caused this collapse. Most people think the most likely reason is that the warming trend continued until there wasn't enough water even in the Indus river valley to support these cities and the farmers who fed them. Some people probably starved to death, while others moved up into the hills, where it was cooler and some rain fell.
But by 1500 BC, the Indus river valley saw an invasion of Indo-Europeans, like similar invasions in Greece and Italy a little earlier.