Counselling for almost all NITs / IIITs (government Institutes) is done through JoSAA except that IIIT Hyderabad, IIIT Banglore,etc. After the JEE Adv results are out, JoSAA will become functional and you will have to register yourself online and follow the other steps mentioned in its brochure.

For other private/ government Institutes, kindly go through the website of that particular Institute and you will find the required details there.