NSD
Every year admission process starts in May and the interviews are scheduled for the end of June.
Let me tell you about the selection process, every year 26 students are selected out of which 13 seats are reserved for different castes. The 26 that are selected hail from various states, say every year only 2 students or a max of 3 can be selected from one particular state (this is not stated in the rules and regulations but this is a fact that you will come to know once you go through the selection process).
To know more, visit the official website of NSD:
http://nsd.gov.in/delhi/Age limit is 20-30 years (for SC ST up to 35 years)
Minimum 6 full-length plays performed.
Some knowledge of direction, stage architecture and lighting is required.
If you have are a trained singer or dancer, it will add wonders to your application.
When you go for the interview, you will have to give a written test first which is a very interesting. (if you have love for theater).
After that, you will be called one by one for the personal interview where they will ask you everything you know about theater. You will have to perform an act and probably they will ask you to sing and dance as well. So prepare one act, one song to sing and also some dance steps.
Note: Make sure that you take your performance CDs and writings when you go for the interview.
I have been through all this process (I was not selected). If you need any help feel free to ask I will be happy to help you regarding any aspect of theater.
FTII
For most of the courses, you need a Bachelor's degree (certain courses like sound Design and art direction need a specific degree).
You can apply online. The admissions usually open around June, keep checking their website regularly for updates. They also announce admission openings in newspapers.
The first process is a written test (at the closest venue provided by them for you). Once you clear that, you need to appear for a personal interview, with a panel of film experts and FTII faculty.
This is the final stage. Clear this and you are officially a student at FTII.
NSD