The Prime Minister of India is

The Prime Minister of India is appointed by the President of India, not elected.
The President appoints the Prime Minister based on the leader of the majority party or coalition in the Lok Sabha. If no party or alliance has a majority, the President appoints the person most likely to secure a majority.

Shri Narendra Modi was sworn-in as India's Prime Minister for the third time on 9th June 2024, following another decisive victory in the 2024 Parliamentary elections.