Visas are required for all except Nepalese citizens.
Tourist visas are usually multiple entry and valid for six months from date of issue (not entry into India). It is easiest to have Indian visas issued in your home country and generally take a week.
Special permits and visa endorsements are required for certain restricted areas including Sikkim. If you are planning to travel to these areas it is best to apply for such permits at the same time as your visa.