All foreign nationals wishing to study long-term at a recognized Indian university or educational institution must apply for a student visa.
A multiple entry visa is typically granted for the entire period of study and the two-month grace period between visits (such as for tourist visas) does not apply. A letter of acceptance or provisional admission letter from the educational institution is required to apply, along with the expected length of the course and proof of financial means/arrangements (approximately Rs 10,000/month of study plus tuition fees). You will also be required to present your passport (valid for the period of study), a completed application form (see local embassy’s website for specified form), 2-4 passport-sized photos and a letter of intention. If you are planning to enrol in a program that spans more than one year, it is recommended to apply for a visa for the full program length, even if holidays between terms divide the academic year and you plan to leave the country during this time. Dependants of those applying for a student visa should apply for an Entry (X) visa.
Depending on the level of recognition of the institution, processing times may vary. Apply at least four to six weeks in advance, however, also check with your local embassy for their specified processing times.
It should be noted that employment is not allowed on a student visa, unlike in some countries, and it is not possible to switch visa types from within the country. You will have to return to your home country in order to obtain a different type of visa.
If the institution you wish to study at is not recognized as a formal place of education and the course duration is shorter than six months, you (and your dependents) can apply instead for a tourist visa. Otherwise, you can apply for an Entry (X) visa.
See http://www.immihelp.com/nri/indiavisa/student-visa-india.html for country-specfic information on applying for a student visa.