There are no direct flights between India and Puerto Rico. There is at least 1 stop to get to San Juan and most of the routes actually have 2. If you're not travelling from the major airports, you might even have a transfer within the country. Several airlines like the British Airways, American Airlines, Turkish Airlines, Etihad Airways and several others operate on routes between India and Puerto Rico.
Puerto Rico's main airport is the biggest airport in the Caribbean. The Luis Mu_oz MarÍn International Airport (SJU) in Carolina is connected very well by flights from several cities in the US mainland and also some major cities in Europe like London, Madrid and Paris.
Ferry services connect Puerto Rico to the US Virgin Islands and the Dominican Republic. These are very popular and scenic routes to get into Puerto Rico.