According to the Motor Vehicle Act, it is mandatory for all motor vehicles to have an insurance (third party at least) before taken into roads. Usually insurance covers a part of all the losses occurred - happened to the vehicle, other vehicle involved and any persons injured by the accident. Third party insurance covers only the last part, ie, the party injured by the vehicle. And at lest a third party insurance is must for a vehicle.
When a buyer buys a new vehicle, the dealer will be providing service of insurance (with their insurance partner) to the buyer. The buyer may choose this or any other at his will. And the period of insurance is of one year and after that usually the company will contact you to renew the policy with updated terms. Again, you may choose this or any other.
And about getting insurance company. All General Insurance Companies do motor insurance. And the prominent ones are United India Assurance and New India Assurance. Of course there are much more.
Get the best suitable policy for your vehicle. Make sure you got the papers before using your vehicle at public roads. And as safety warning, Always wear Helmets/Seat belts!