The Homestead Act of 1862 allowed any US citizen to stake out 160 acres of Federally owned land. Provided that the citizen lived on that land and improved it, they would own the land, free and clear. By 1889, most of the land that was worth farming had already been settled. The last really large chunk of prime unsettled land was located inside the Indian Territory. On April 22nd 1889, the Oklahoma Allocation Act opened up 8000 square kilometers (Two Million Acres) for homesteaders. They had to line up at the border and race into this territory to stake out their claim. Some people jumped the gun and staked out their farms a few days early. They were known as "Sooners" and the Oklahoma University Football team is named after them. The best fictional account of the events on April 22nd 1889 in Edna Ferber's novel Cimmeron, from 1929. The town of Oklahoma City and Gutherie literally sprang up like mushrooms. Those two towns had their town plots laid out, a town government established and a population of 10,000 people by the end of April 22 1889. So, in one specific incident, that was exactly how it happened. There were future openings of other parts of Oklahoma, prior to 1907, but these subsequent events were smaller in scale and much less hectic.
For more details about the five land grants that settled Oklahoma between 1889 and 1907, check out
http://www.okgenweb.org/~land/