A car is the second most expensive thing Indians will buy, the most expensive thing being property. Unlike property, a new car is a heavily depreciating asset that also requires investment. There's annual maintenance, an insurance premium, fuel bills... and repair through damage caused by other people who use the roads.
At this point, I must state that this article is for those whose vehicle gets damaged through no fault of theirs; if you end up damaging someone else's vehicle, just do the right thing and pay for their repairs, will you? Moving on: insurance is an odd thing in India, and it doesn't work the way it should, which means that you need to figure out a different way to settle your dispute with whoever has damaged your pride and joy. Remember that what I write here is in no way legally correct procedure; it is simply what works.
1. Take photos of the cars immediately. If nothing else, you'll require them for your insurance claim.
2. Establish firmly that it was the other person's fault (if it really was, of course)
3. Confiscate their keys and driver's licence. Yes, this is quite far outside the bounds of the law, but without this, the other person literally has nothing binding them to pay up.
4. Say that you'll deposit the car key and licence at the nearest police chowki, where you'll want to file a complaint for insurance purposes.
This is an idle threat, because the police will not want to take the complaint. It is needless paperwork in their eyes, and you'll have to bribe them one way or another if you reach that spot. Second, if they actually do the work, both vehicles involved in the incident now become potential evidence and as such will be required to be presented in court - if proceedings get that far.
I have a friend whose car got stolen and then recovered, but the case hasn't got a verdict yet. Therefore, this 25 year old car sits rotting in a garage, forgotten, simply because the law doesn't allow its ownership to be transferred while it remains evidence in an active case.
If the person tells you to claim insurance, point out that you'll lose use of your car for that many days, and ask them to reimburse you for those days lost. Then you'll lose the no-claim bonus, which is an increasing percentage year on year, and impossible to calculate because insurance premiums rise every year. Finally, the value of your car will depreciate because the insurance record will show that you made an insurance claim - meaning that your car had got into an accident.
In conclusion, in some areas we're still very much the wild west. The law doesn't work in the favour of the righteous, and you've got to work with whatever you can, rather than what you should.