Find out who owns mineral rights by going to the local courthouse in the immediate area and looking in the land title indices located there. Once you find the index containing your property, you must find every single person who has owned that property since the government started keeping records on it. This is rarely a straightforward process, as mineral conveyances are often listed in wills, divorce settlements and other bequests that are not always recorded in title indices.
To prove beyond all reasonable doubt that you are the owner of the mineral rights under your property, you must provide a full, unbroken history of every conveyance, meaning the times in which the mineral rights have gone from one individual to another, that has ever taken place for that property. If you come up with any gaps in the mineral rights history, there will be some legal doubt as to whether or not you are the undisputed owner of those mineral rights, even if the gap is over a century in the past.
Because finding a full, unbroken history of mineral rights for any given property is an extremely frustrating, difficult process for anyone other than a legal professional, many people trying to prove their claim on a property's mineral rights turn to lawyers or landmen to "run their titles." Having a professional run your title for you is certainly much easier and potentially faster than trying to assemble an entire history yourself, but it is much more expensive, and there is no assurance the professional can produce a full, unbroken title history.