If have plans to do Ph.D. research in India, chances are you already know how to get there. Maybe you're being funded with a Fulbright-Hays DDRA--in that case, USEFI will probably be taking care of a lot of your details. Or perhaps you have an AIIS Junior Fellowship--in that case, you can rest assured that the people in charge of administration definitely know how to get you in and out of the country. However, I've met a few grad students who decided to do research in India at the last minute, so here's some hopefully helpful advice.
I wouldn't recommend planning a lengthy research trip to India if you've never been there before, and in fact, Overseas Research: A Practical Guide recommends you take at least one reconnaissance trip to your area of research before committing to a long-term visit. An "easy" way to test out India is to participate in a language program. I myself did two Hindi language programs through AIIS in preparation for my doctoral research.* Of course, this meant I had to plan ahead, and spend two of my summers away from home. I recommend others take this route, though. If you study in India for a couple of summers, you will having something to put in the "previous preparation" section of fellowship applications, but more importantly, your stress levels will drop dramatically when you start thinking about long term research abroad. You'll have a better idea what you're getting into if you visit for awhile first. Even if you have to spend your own funds to take a quick, three-week vacation in Delhi or Mumbai, I'd recommend you do it, just to get your feet wet.
Obviously, the best way to arrange for research in India is to land a Fulbright-Hays DDRA, Social Sciences Research Council-IDRF, or AIIS Junior Fellowship. Still, you should be able to manage a trip if you have department or university funding. India now outsources its visa processing to Travisa, and you should check those very helpful pages rather than believe what I say, but here's my bit of advice. If you're going to be staying only a few months in India, you can probably get by on a tourist visa. As the India Department of Education says, you can still conduct research while on a tourist visa. Tourist visas are typically only good for six months, so your trip would be limited in duration. If it's your first trip to India, that might be a good thing. To be quite honest, I wanted to come home at the 6.5 week mark on my first trip, and at the 8.5 week mark on my second. So, you might want to plan just a 1-2 month trip the first time, anyway.
If you want to stay longer than six months, the first thing you should do is check to see if your university is affiliated with AIIS. If your university is a member institution, AIIS can help you obtain a research visa! A lot of people don't seem to know this, or think they shouldn't bother the people at AIIS, but that's why your university joined this organization, to help out students like you. You should keep in mind that obtaining a research visa can take up to six months, so contact them in plenty of time. AIIS can help you arrange for a certificate of affiliation, a necessary piece of paper to get a research visa. My certificate of affiliation with Jawaharlal Nehru University in Delhi was arranged by USEFI, but I did a lot of emailing beforehand, making sure I had already introduced my research project to faculty in appropriate university departments. I think this is a crucial step: go ahead and e-mail these complete strangers and talk to them about your work. Really, you should do this. It can be a lot of work (I sent more emails that bounced back undelivered than I could even count), but it's good to have potential faculty contacts, and more importantly, some really interesting and helpful people.
No matter what, the process is expensive (I paid a total of $397 in fees for photos/passport renewal/research visa processing). Since everything takes so long, you're going to want to budget for overnight mailing. You're going to do a lot of photocopying (the research visa requires seven copies of the "proforma," a data sheet stating who you are and what type of research you want to do).
One thing I didn't know about until pretty late in the game is obtaining IRB clearance. As a historian, you probably won't be working with human subjects. Still, my fellowship required IRB clearance, so I had to apply for an exemption. I didn't even understand the questions on the form, actually--I presume they are clearer to people who regularly conduct ethnographic or sociological research, but I had to have several conversations with the IRB representative on campus before I had the form filled out properly. So, this might be something to get to work on right away.
*There are many other options for language programs, of course. If you are interested in Bangla, you can go through AIIS, but you can also apply to go to Dhaka through the American Institute of Bangladesh Studies. UC-Santa Barbara runs a Panjabi studies program in the summer. You can seem some other choices at the University of Chicago Summer Language Resource Center.