Get a passport. It can take up to 6 weeks to process a passport application. See the website below for full passport details. Obtain a visa. All visas' to India are now processed by Travisa Outsourcing and can be done in person at the embassy or online through their website.
Check the Department of State website for any current travel restrictions. Purchase a ticket to the destination city(s).
Check customs and duty restrictions as well as baggage restrictions for the airline as well as the TSA's website.
Pack for the trip. Most of India is hot and humid the majority of the year. It could also save time and effort to purchase a passport wallet to keep items that you will need to present at each stop during the trip such as your passport and plane tickets.
Plan to arrive at the airport at least two hours before the flight leaves. Due to the duration of the trip, be sure to wear comfortable clothing.