Hello Venkata

First of all, congratulations on qualifying the JEE examination!!

The JoSAA counseling usually starts within a week after the JEE advanced result has been declared. Since this year the result was declared on 14th June, tentatively the counseling will start from the second-third week of June. To make sure that you don't miss the date, keep checking the official JoSAA website. Also, you can refer to the Careers360 portal so that you don't miss any updates regarding the same. 
Hope this helps.
All the best!!