Dear Subhash,

After qualifying GATE exam, and receiving the score card, that mentions your score and your rank, you need to sit for councelling sessions for various institutes. There are two ways for that.

• GATE COAPS: This is the councelling portal for admissions to IITs and IISc Banglore. You will have to register yourself for the same by going to the following website.
  http://coap.iitm.ac.in/
  Once you have registered, into the portal, you need to fill up your choices (what program you desire to join into). Once you are finished with that, a cutoff will be announced and after that you will be alloted a seat in that institiution. 
  Many of the branches in M.Tech/M.S./PhD in the IITs and IISc intake students only after taking a seperate test/interview. For this procedure, you will be shortlisted and called for test and interview by that department. If you clear it, you will alloted the seat and asked for paying the admission fees.
  
  
• GATE CCMT: This portal is for admissions into all the NITs and IIITs on the basis of GATE score. The procedure is the same, you will have to register on the following website,
  https://ccmt.nic.in/webinfo/Public/Home.aspx
  fill up the seats and as per your choice and wait for the cutoff to be announced. Once that is done, you will be given choices as per your choices and cutoff for various institutes, you can either opt for admission by paying the fees or you can attend further councelling sessions.
  
  
• Direct application on institute website: You can also directly apply for admissions by visiting the institutes website and registering onto them, paying the fees and applying into the program of your choice. There are only some programs that are considered with COAP, you will have to directly apply into the institute of your choice. For examply here is the list of websites for some of the IITs and IISc Bangalore.
  IIT Bombay:https://portal.iitb.ac.in/mtechapp/mtechAdmissionLinks.jsp
  IISc Bangalore: http://admissions.iisc.ac.in/Web/Login.aspx
  IIT Delhi: https://ecampus.iitd.ac.in/PGADM/login
  IIT Madras: https://research.iitm.ac.in/
  
  Similarly you can also visit the institute of you choice and fill up the application form.
  
  You can also check GATE cutoffs for admission to various institutes here
  
  https://engineering.careers360.com/articles/gate-cutoff
  
  https://engineering.careers360.com/articles/gate-cutoff-for-nits
  
  https://engineering.careers360.com/articles/gate-cutoff-for-iits
  
  Hope this helps