Yes, most hunters hunt on other than their own property.
As for the license, you don't need land, or even a gun.
You get a gun safety course with hunting in mind (hunters safety course) often available at a local sheriff office or through the NRA and you are good to go.
Preparing for the hunt, you get your tags (technically your license) Select a hunting location you can legally hunt, then get your limit per tags. I don't know of any state that doesn't have some hunting areas and there are private hunting lands you can use by permission. State/national parks would be out, but any open BLM land is free to hunt on. Check with the BLM or local ranger office, they can tell you.
But always check in advance and stay within laws.