So someone else can drill under my land?
Isn’t that what Hussein said the Kuwaitis were doing to Iraq?
If you lease them your mineral rights.
If you lease/sell them your mineral rights.
You’re getting a lot of different answers to different aspects of your question.
Do you own the surface rights AND the mineral rights to your land?
If you only own the surface rights, and someone else owns the mineral rights, they can indeed drill under your land and often right ON your land...owning the mineral rights can also mean owning the right to access those minerals.
If you own the land and the mineral rights under the land, then no one can take your oil, etc., without you signing a lease.
If you have mineral rights and are offered a lease, go slow, check around, see what things are worth. In my area people signed leases for $15/acre before the boom came on, and their neighbors who waited got $500/acre or more.
After you sign a lease, if you do, then the company that leased the rights usually has a specific period—three years is typical—within which to ‘prove up the lease, in other words to go in an drill or mine, whatever.
If they don’t, the minerals revert to you. If they do drill, then the lease is good (I THINK BUT AM NOT SURE) for the life of the well. There can be wrinkles in this also...they might drill, and tell you there is no oil down there, but the lease still will remain valid for them, but again I’m not sure for how long. (I know of wells that were drilled and capped, and then a couple years later the company was suddenly (!) able to get them flowing.
You want to be careful about signing a royalty agreement too. They vary in terms and payouts and so on. Try to find out what the highest percentage of the well output you can get for yourself. Some states have an upper limit for the mineral owner (you) but even then oil companies might try to get you to sign for something lower.
Go slow, talk to your neighbors and to local officials, maybe even a lawyer. Go slow, be wary.