This, in reality, is a very complex question. International interns come to India on many different types of visa: Tourist Visa, Entry Visa, Employment Visa, Business Visa or Student Visa, not one of those being applicable to all internship situations.

The Entry Visa (X Visa) is generally for those whose purpose of visit India does not fit into some of the typical visa categories, such as people coming for short term classes, volunteer work, or unpaid internships to India. You should apply for an Entry Visa and a copy of the offer letter saying the terms of your internship place. If you're a student and the internship is part of the research you also need to obtain a letter from the college describing why you're likely to India.

Internships with a "stipend", allowance or salary are generally considered to be paid internships and these technically require an Employment Visa (which requires additional documentation like the employment contract and a proof from the employer that no formal Indian federal could be found to fill the place). However, many organisations may directly ask you to come to a Tourist Visa because it is simpler for them and also for the applicant - despite the fact that it is technically legal.

Before applying for all types of visa make certain your passport is valid for 6-18 months, depending upon your specific visa. Applicants who are not citizens in their country but taxpayers must send a copy of their residence permit with this program. It's always advisable to consult the various embassy in your own country, for instance the Indian embassy in Spain, Germany, Italy etc.. There you will find most of the information considering your visa.