Did your ancestor homestead? Ancestry.com/ has many homestead records for land that opened up in America in the 1800s. NARA has this short primer on the 1862 Homestead Act: http://www.archives.gov/education/lessons/homestead-act/
Now that you're up to snuff, try putting your ancestor's name in the search engine at the marvelous Bureau of Land Management site: http://www.glorecords.blm.gov/search/default.aspx Did you find him or her? Is this cool, or what!
In 1930 my Great-Grand Dad was issued a land patent near Hagerman, New Mexico for the purpose of "stock raising." I knew he loved and raised horses, but didn't know he raised cattle. Or did "stock" also apply to horses?
"Patent # NMLC 0028040 is a homesteading, mining, ranching, logging, and more patent in Chaves, New Mexico owned by John W Coffee. It is a homestead entry: stock raising."
"Ownership and use of this patent is overseen by the Bureau of Land Management's Roswell Field Office under the serial number NMLC 0028040. The last action for this patent—patent issued—occurred on May 20, 1930. Information on the patent was last updated on July 19, 2011."
Seven years earlier, In 1923, a New Mexico land patent was first issued to John W. Coffee. Why wouldn't they also list his wife, Dorothy? Was that not a thing back then? American women had won the right to vote just three years earlier. But considered "chattel" in many states for decades to come.
Some time after their marriage in 1904, Dorothy (McCormick) and John W. Coffee moved to New Mexico Territory. They appear on the 1910 Federal Census in Chaves County with their infant, Audrey. New Mexico became a state in 1912. They farmed in Chaves County until 1940 when the census finds them in Fort Sumner, DeBaca County. That census page indicates an address of: "Left Side Of 4th Valley Road." My mother recalls their home being in baseball-batting distance to William H. Bonney's grave. You know, Billy the Kid.
In their seventh decade and during World War II, my Great-Grands joined their children in California. Dorothy passed away a decade later, and John lived to see his 93rd birthday. I don't know that they ever returned to New Mexico to visit.