You will need a visa to enter and stay in India, and the nature of that visa must suit your pursuits here. It is important to get the right visa, and unfortunately, information that can help you decide what you need is hard to come by.
Your best bet is to talk with the local Indian Consulate in your home country and clearly explain what you want to do in India. Different countries have different bi-lateral agreements with India regarding visas, though there are similarities. You have to determine the requirements for your case to avoid complications when you get here.
The following is visa information of a general nature, applicable to citizens of many Western countries, but there are differences by country. For example, Americans can now get up to 10-year business and tourist visas, with valid documentation
With validity of six months from date of issue. Longer issues - one to five years - are possible, depending on circumstances.
Business visas are for people exploring opportunities or setting up business ventures in India and are usually for one year but can be granted up to a maximum period of five years. Applications for business visas should be accompanied by a letter from the applicant's company stating the purpose of the visit.
For people undertaking employment in India. Information on this category is hazy. Some Consulates don't mention it at all, but it seems to exist, and appears necessary for people who will be working here, for either a foreign or an Indian company. Ask at your local Indian Consulate.
Issued to people of Indian origin and people who's spouses are posted to India on company business. Normally one year, extendable in India, but possible to a maximum of five years.
Up to five years. You should present a letter of admission from a School/Institution, either in India or abroad.
Good for 72 hours and up to two entries. It is not clear if the two entries must happen within the 72 hours, or can total 72 hours over a longer period. Ask, if it is a problem. If you will only be stopping in India and not leaving the transit lounge at the airport, no visa would be required.
Though you can extend a visa once you are here, it is better to get one that covers the full length of time you will be here, or at least as long as possible. If you come in with a multiple entry visa good for one year and then extend that for another year, you will not have multiple entry privileges on the extended time. If you leave the country, you must get a new visa.
If you stay here more than six months, you will need to register with the local Foreigner's Registration Office. Most large cities have one, but smaller places may necessitate a trip. The process is quite bureaucratic, and you'll need two photos and may need to pay a fee. You will have to go in person. (Take a book to read.) You'll be issued a paper, or booklet, that is proof of residency. If nothing else, it should allow you to avoid the extra costs of paying for foreigner's prices for fancy hotel rooms, and maybe even for domestic air tickets.
Not all offices seem to be up to date on regulations. If you leave the country after being here for more than six months, you may have to get a "no objection to leave" certificate, or some kind of clearance. However, you may not be asked to show that at the airport when you leave. It is usually best to humour the wishes of the local officials. Find out what they want.
Foreigners are also required to register as such when they check into hotels. This is a lingering bit of bureaucracy based on the Registration of Foreigners Act of 1939 brought in by the British to control enemy aliens during the Second World War. That it is in force today is indicative of the general suspicion and paranoia the Indian government still has towards foreigners. In this age of globalisation, with foreign businesses being encouraged to set up in India, and with literally millions of Indians venturing overseas to enjoy relatively hassle free hospitality in host countries, it is hoped that the government here will review some of the out dated restrictions still enforced.
Another odious requirement is that any foreigner staying more than two years must undergo a test for AIDS at a Government Hospital. If this is to prevent the virus coming in, why wait two years? Besides, India is projected to have one of the highest HIV infection rates in the world, and getting tested at a Government Hospital may well increase your personal risk.