Note: most of this was written late 2017 and may not be up to date.
Being a postdoc at TIFR is a quite enjoyable experience, but surprisingly the news are only slowly trickling outside the country. This means that information can be hard to find at times, not because the topics are complex but because they are so obvious that nobody thought to mention them, that is obvious to all but a bewildered foreigner who is not in the knowing. This is to say, the best source of information are the locals, who will happily answer all your questions, but there are going times when you do not know you should have asked. The following notes are a collection of my own experiences, focusing on those times.
There is no application period, so it is enough to contact your prospective host to get the ball rolling. Doing so five months before your intended starting date should work.
If you get an offer and accept it, then various government departments will have to give their approval. After that you should apply for a research visa. The requirements are fairly arbitrary and can depend on the visa centre / consulate, even within the EU. To give an example, one consulate asked me to provide an extensive research plan, not unlike a grant application, while another asked for a copy of my thesis plus approval from another set of government departments.
An important administrative detail, both for visa and tax purposes, is that you are not going to work. You will receive money to support yourself, have health insurance and other benefits, and be treated as any other employee as far as TIFR is concerned, but legally you are in some other category. It should not affect you too much, but you may want to say “I do research at TIFR” rather than “I work at TIFR”.
You should fill a form online before visiting a visa application centre, and then do so armed with all the documents you have and some more. Having one separate document for each document the embassy requires will make things smoother and can save you some back-and-forth trips; it is even better if they have the same name since the staff at the visa application centre does not like deviating from their scripts. Filling the online form is tedious but not hard. You will be asked for your religion; I had no trouble telling the truth. It is likely that there will not be enough space to list all the countries you visited in the past, but limiting myself to countries for which I had a stamp in my passport plus a choice of my most recent visits worked.
When flying in, keep in mind that Air India has a very generous baggage allowance.
You will get a detailed list of instructions on how to do all internal paperwork you need to register with the institute. It is accurate and up-to-date because it is used often.
Try to get an Indian phone number as soon as possible, this is as soon as you have some document you can use as proof of address. It can take about a week for the SIM card to be activated, and while it is not strictly needed, it will make later paperwork helpful. According to the locals, the company with the best signal on campus is Airtel. If you choose it, then buy your SIM card at their official store in Fort; while there are closer stores to campus, they are not familiar enough with the requirements for a foreigner-owned SIM and will make a mess of it.
Make sure to obtain a residence permit/certificate at most 14 days after you arrive. You cannot exit the country without it, and you need to produce it at the border when leaving and reentering. These days it is enough (and possibly mandatory) to do so online using the eFRRO service, and this most likely requires a local phone number. Do not rely on the official list of documents but use the help of the TIFR public relations office to know which documents to submit; in particular you should probably add an Undertaking Form and “Form C” as Additional Documents.
To open a bank account you will need a PAN card and/or an Aadhar number. Indian citizens must have an Aadhar number, but rumour has it that the biometric data linked to Aadhar is not properly secured, therefore I avoided getting one. Keep in mind that the goverment is strongly pushing Aadhar and it might soon become mandatory. You can get a PAN card with UTIITSL. Their nearest physical office is at the 5th floor of an unmarked building; Google Maps may have old data.
When you open your bank account, make sure to ask for net banking and to link your phone to it. You will instantly get a RuPay card, but that is useless outside India and sometimes even inside, so I would recommend to apply for a Visa/MasterCard in addition and ditch the RuPay card once the useful card is ready.
There will be a bit of paperwork before leaving, but by this time this should be no big deal. One piece of warning: in order to close your bank account and transfer your funds abroad you will need a chartered accountant to certify that your income was legally obtained and that you are in good standing with the tax agency (which you should since your income was tax exempt). I asked among the faculty for an accounting office they would recommend, and mentioning who referred me the first time I called the accountants made things very smooth.