How was India discovered?
The question as phrased is ambiguous. However, when discussing routes, it is stated that Vasco da Gama was the first European to reach India by sea in 1498. It should be noted that land trade routes to India were already developed before da Gama’s voyage. European empires had been trading with India through the Silk Road that provided a crucial link between the East and West.
The routes over land were marred by great challenges due to territorial disputes, making it dangerous for traders. The situation forced the different European administrations to seek out alternative routes. Portugal arranged and commissioned da Gama’s voyage, which saw his fleet travel along the western coast of Africa to the southern coast. He eventually reached Africa’s east coast and hired an experienced Indian navigator to guide his fleet to India.
India never needed to be "discovered." A land route known as the the Incense Road was used in ancient times by the Egyptians and Romans, connecting the Mediterranean to India.
In 1497 Vasco da Gama set off on the first ocean journey directly from Europe to India. Other explorers had made it around the Cape of Good Hope, but Gama was the first to successfully cross the Indian Ocean and make port in Calicut. In that sense, Vasco da Gama was the first to discover a sea route to India.
People in India have been living for more than 50,000 years. There was really no need for India to be discovered by the natives of India, at least not for the last 50.000 years.
Also India has been a well known country among many other countries for many thousand years. How and when people in each of these countries discovered India is not known to historians. All that is known is that India started trading with other countries many thousand years back. Indications of India's trading links are available in its ancient books. For example Mahabharata the biggest epic in the world written many thousand of years back, has mentions of many countries and the goods that India imported from them.
If you are talking about discovery of sea route from Europe to India, this was discovered by Vasco de Gama in 1498.