Generally, the process of finding unclaimed land in the US and acquiring it for free is called “homesteading.” Homesteading laws were introduced to transfer vacant land owned in the public domain to private ownership, but these laws were repealed in 1976. Today, any such land has to be classed as “unneeded” by the government to be available to the public. Although it isn’t as good for the would-be homesteader as in the old days, you can still grab some unclaimed land at a decent price through the official channels.
Contact your state’s Bureau of Land Management office. If there isn’t one listed for your state, choose the closest one to you. Ask BLM representatives if they have any information on publicly-owned land for sale in your area. There aren’t very many patches of land available anymore, as the Federal Land Policy and Management Act of 1976 states that public land should be held in public ownership. They do offer some land for sale, but it is often agriculturally useless.