You might want to start by calling the Cemetery and seeing if they will give you any info over the phone. They might charge for info on their graves but I have been so lucky with some Cemetery's that they gave me so much info and others want money and will send you a report. I don't think you will get Mother and Father's name (try getting a copy of the death certificate for Mother & Father's name) but you will get birth date, death date even cause of death it all depends on what info the Cemetery collects. You will also get who is buried in the plot. Also, try Find A Grave on the internet. You can search by name and sometimes you will find your relatives info and picture of grave stone.