How did Islam come to India?
Islam came to India through both peaceful and violent means. It came peacefully through traders and violently through invasions.
Islam came to India very soon after the faith was founded. Even before Muhammad, Arab merchants had been trading with people in the west coast of India. Not long after Islam was founded, most of those merchants were Muslim. These merchants sometimes settled in enclaves along the coast and set up little communities that were Muslim. A similar thing happened with overland trade in some parts of northern India. In this way, Islam came to India with peaceful Muslim merchants.
However, Islam also came to India through violence. It came along with Muhammed Ibn Qasim who invaded part of India in an attempt to punish pirates. In the early 700s he established control over much of the Indus River Valley. Islam was further strengthened in India some centuries later when Mahmud of Ghazni invaded from Afghanistan in the 11th century and when Muhammed of Ghor did the same a century later.
In these ways, Islam came to India both through peaceful trade and through violent incursions. (My source for this answer is Religion in India: A Historical Introduction by Fred W. Clothey, 2006, p. 125-7.)