Hi
You can start by researching in the county clerk records. Sometimes you can pull documents online at texasfile.com. You can search your parents name to pull up any documents to review. Then the previous owners name and so on until you get a clear picture of what was sold or kept throughout the years. (like a family tree but for minerals)
Then you can take the legal descriptions (location of the minerals) that are contained in the deeds and search on the Texas RRC website to see if there was ever any production on the land.
Finally you can search unclaimed property websites for the state of last residence or State of Texas (claimittexas.org) to make sure that no funds were ever sent to the state.
You will also need to file appropriate documents in each county that show the land passing from your parents into your name (probated will, affidavit of heirship, - differs based on different circumstances). You may want to hire an attorney or mineral consultant to help with this part.
Good luck!