Hello.

If you want to apply for PhD in IIT then you have to fillup the Gate exam form available at gate.iitkgp.ac.in, fill in the details , upload the required documents and submit the form. You have to qualify the GATE written exam and if you do ,you have to face the interview round. If selected, you'll be able to pursue PhD at IIT.

Another option is that you can directly apply for IIT through NET qualification.