I would claim private property to avoid the Government from claiming "Eminent Domain". Then, I would hold off and spend the money I would make promoting reusable energies that are better than fossil fuels, particularly on the wallet and the environment.
Assuming that I had the mineral rights, I'd contact an oil company and arrange a lease. It's not likely that you could ever discover oil on your own though, since most is found thousands of feet below the ground. Some of my hubs are about how oil wells are drilled, if you are interested.