JoSAA counceling is entirely an online process.
Once JEE Main and Advance results are declared, you have to register at JoSAA portal.
Then you are asked to fill up your choices of colleges and branch. Name of colleges and branches are already fed up in the portal . You have to just choose them in order of your preferene.
Those who have cleared advance, will be shown the choices of IITs, otherwise choices of only NITs, IIITs and GFTIs are displayed on portal.
You are allowed to keep a mix of IITs , NITs , IIITs and GFTIs in your preference list. You can choose upto 600 courses.
Before a certain date you are supposed to lock your choices. Once choices are locked, you cant change it any more and this preference order is valid for entire councelling process.
Even if you dont lock, it automaticaly gets locked at certain cut off date and time after which you cant change. So be sure to recheck your choices before locking and befor cut off date.
Then different rounds of allotment take place , usually 6-7 rounds.You are allotted a branch in colleges as per preference and merit list.