Train, bus, and flight are the preferred modes of transport in India. For short distances, it is better to take a bus or a cab. For long distances, you can take a train or a flight. Waterways are not well developed in India.
It is a good idea to contact a travel agent to book tickets (travel in India is confusing because of the multitudes of trains and buses). You can also book tickets yourself via online portals like TicketGoose, RedBus. Ibibo or MakeMyTrip. To book rail tickets, log on to irctc.com (Indian Catering and Tourism Corporation Ltd.), a government owned enterprise. Most of the larger states have their own road transport corporations, which also have websites.
Ensure that you book your tickets well in advance because seats tend to get filled quickly. Please note that both buses and trains have special arrangements for women (separate seats for women on buses and separate coaches for women on trains).