In India
You need to have a bachelor's degree (3-year course) or equivalent in any discipline recognised by any Indian University / AICTE as eligible for post-graduate studies.
You can apply while you are in your final year of graduation. If you do get through the admission test, you will be given provisional admission on the condition that you provide your mark sheet and a certificate of passing by a certain date.
US & Europe
The basic qualifying exam for doing an MBA outside India (US, Europe, Australasia) is the GMAT (Graduate Management Aptitude Test) conducted in centers across India.
After you get your GMAT results, you need to apply for admission to specific institutes. There is normally no GD or Personal Interview process (like in India) - however, different institutes have different processes and criteria for admitting students.
Selection process
The most sought after institutes have their own independent admission processes.
However, all of them have a 2-stage process:
Stage 1: Written admission test.
Multiple-choice tests in maths, verbal, reading, logic & business awareness conducted in centres across India.
Read more about specific admission tests
Stage 2: Personality Assessment
Those who qualify through Stage 1 normally proceed to two stages of personality assessment:
Group Discussion: Your performance in a group, while discussing a topic of current importance, is evaluated by a panel of judges. Read more about GDs
Personal Interview: You are interviewed by a panel of specialists. Read more about the interview process .