For transferring the ownership of the car, you would have to fill and submit following forms to RTO -
Form 29
Form 30
The forms have to be filled up and both of the parties (buyer and seller) would have to sign and the buyer would have to submit them at the local RTO with the Original Registration Certificate and attested photocopies of Insurance, proof of address and Identity proof. The seller will get the acknowledgement of the transaction from the RTO within a week and the buyer will get the new RC in next 15 days.
After transferring the RC, follow the procedure of transferring the insurance as told by Expert.
Please let me know if you have any questions on the same.
Hope this helps