[A2A] I had recently answered a similar question:
Brijesh Kumar's answer to How is a typical interview process for professorship at tier-A science/engineering institutes in India?
You apply by going to the website of each IIT. Applications are open throughout the year. Then you get shortlisted based on your resume. Department calls you for a talk in front of other faculty in the department and/or a teaching session in front of students and/or faculty, based on which you are shortlisted further. Then, you are called for a final formal interview with the director of that institute, HOD and 2-3 external experts (usually from other IITs or industry). In the interview, they could ask you anything ranging from your research and teaching plan to HR questions like why that particular institute. If you pass the interview, you are made an offer to join that institute. Good luck.
If you are outside India, depending on each IIT's rules, you may be able to do interview and/or department talk via video-conferencing.