Generally, the process of finding unclaimed land and acquiring it for free is called "homesteading." Homesteading laws were introduced to transfer land owned in the public domain to private ownership, but these laws were repealed in 1976.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.
Find out as much information as you can about the land available. Travel there if you can. Because homesteading is no longer a free process, you need to determine whether this land is suitable for your needs. If you wanted to build something on it, think about the lay of the land, and the size and shape of the plot. The government wants to keep hold of the land, so the patches offered up for sale are often in disrepute.
Find out when the land is being offered for sale. Land is usually sold by auction, which could be either sealed or open bidding. On occasion, the land will be directly sold to an individual, or auctioned with preference to nearby landowners. If the land is very close to your home, or land you own, you can speak to the BLM directly about this, but the chances are you will have to attend a public auction. The auctions are likely to be held relatively close to the plot.
Think about going further afield than the U.S. if you want to claim land for free. Of course, in the developed world, there isn't much land that hasn't been claimed by somebody, apart from uninhabitable or remote locations. Technically speaking, it is possible to claim land for free if nobody has ever wanted it before, but any land that has gone unclaimed throughout history is probably in no way practical to own.
Good Word USA: "Homesteading: Land From the U.S. Government?"
Bureau of Land Management: "Homesteading"
Good Word USA: U.S. Bureau of Land Management Contact Information"
Johnson, Lee. "How to Find Unclaimed Land." , https://legalbeagle.com/7262013-unclaimed-land.html. Accessed 19 April 2019.
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