Not had this experience to comment on this first hand.
But as an Indian, I guess they ask you to surrender your Passport at the Indian embassy, and then ask you to apply for a PIO(Person of Indian origin) card.
One way is when we enter India at borders, they check out exit dates in system. Usually people who are still indians would have US's some kind of visa. US Citizens will not be able to show any US visa.
There are heavy fines for not self surrendering the indian passport after US Citizenship within 6 months.
Not had this experience to comment on this first hand.
But as an Indian, I guess they ask you to surrender your Passport at the Indian embassy, and then ask you to apply for a PIO(Person of Indian origin) card.