Hope you have a bunch of money to waste because it is a lot more complicated than just knocking a hole in the ground. Statistically, only 1 well 10 is actually a producer and the payback period can be years. Your odds increase if you are in an oil producing area and are surrounded by other wells but I doubt that you are. If any of the field was under your property, you already would be recieving royalties. You don't actually need to have a well situated on your property to recieve royalties if the field is unitized, which most are.
Firstly, you have to own the mineral rights. Lots of people sell land but retain the mineral rights so just because you own the land doesn't mean you own the rights to any minerals under that land.
Secondly you need to find out if there is any chance of oil being there in the first place. The chance of drilling a hole and finding anything through blind luck is non existent unless you are Jed Clampett. That means hiring a geologist to map the place and depending on his opinion, shooting seismic and hiring a geophysical company to interpret the results. You've already spent a bunch of money and haven't drilled a foot yet.
If there is the possibility of something being there, it all depends on how deep it is and what pressure it is under. Deep, high pressure wells will cost anything from $2 million to $4 million and take 2/3 months to drill. The most expensive land well I drilled was in the Amazon jungle of Peru and cost $40 million ... and there wasn't enough there to be commercial. Now you know why gas costs so much. If it's real, real shallow and no pressure, you can probably get it drilled for about $50K in a few days. The rules and regs governing drilling for oil/gas vary from state to state and those can double or triple the drilling costs.
Then you have all the costs associated with testing and producing the stuff if you find anything worth keeping in the first place.
This is getting rather long, so let's just say that your chances of finding anything without experience or specialized training and knowledge is NIL.
What most small independents do is to find and develop a likely prospect, put together a package and try to sell that package to investors or larger oil companies with the resources to drill, retaining a percentage for themselves to cover their costs for the initial work and provide a profit if the well comes in.
Sorry to be so negative but all the easy stuff in the States was probably found a long time ago.