How does the application process work? What sort of time frame are we looking at?
Time-frame: begin making your enquiries 2-3 years before you actually want to move. Better still, try to arrange informal visits or seminars (that are not necessarily job-talks) AS SOON as you are nearing the end of your PhD or beginning your post-doc. Institutions are quite friendly to visitors who write saying "I'm coming home on vacation, and I want to begin to explore options of returning to India after my post-doc is over, may I visit and give an informal seminar?" If you don't have work that suits a seminar, give a lab-meeting style presentation hosted by a faculty member in your field, to which a few other faculty may come. This will help the department see your work evolve in subsequent years, and they will have a better background for your job talk which may be 4 years later! Also, practically, an informal early visit will give you a contact you can write to later on when you mail a formal application.
If you have NOT made initial visits and want to move back on a quicker time-frame, that can also work. Its not as if paperwork necessarily takes so long- appointments can be made on a 6 month timescale depending on the procedures at particular Institutions (others are known to take much, much longer- this needs to change, obviously, in order for them to remain competitive in terms of attracting back talent). We suggest you make contact early only so that you can explore more carefully where you might fit in best- unlike the US, Institutions in India vary greatly on how things are run- so its worth it putting in the effort to visit them early on. If you don't have as much lead-up time, just write to as many places as you think you might reasonably want to visit, and plan a job-talk tour giving talks everywhere. In your initial email, you can indicate that you are planning a trip to India at time X, and would be happy to give a talk at that time. Also state the time frame you want to move back in- it helps the Institution respond.
The application process: Apply with a CV, names of referees, and a research plan. If you are continuing aspects of your postdoctoral work, be certain to have a good response to the question "how will you distinguish yourself from your postdoctoral mentor".
Your application will be evaluated, letters of recommendation will be solicited (often a greater number than at US Institutions- provide at least 6 names if possible, and the Institution is likely to seek letters from additional people who look at multiple applications over time, for reasons of comparison and consistency). The evaluation process involves a few different levels of committees- it is best to ask because this varies depending on the policies of each Institution.