Answer
The process is called “eminent domain,” and generally it involves acquiring private property for a public purpose, such as a new city reservoir. If the city can't come to terms with the property owners, it can use its power of eminent domain to force the owner to sell. In theory, the city pays fair market value, since the Fifth Amendment to the U.S. Constitution states that "nor shall private property be taken for public use, without just compensation."
But federal land (nearly 65 percent of Utah's 84,916 square miles) is public property, not private, and the Constitution also states that "This Constitution, and the Laws of the United States which shall be made in Pursuance thereof ... shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding."
With the "supremacy clause" making it pretty clear about who's in charge, why is Utah challenging the feds on land ownership and usage?
There are two answers. One is that this is just a continuation of Utah's long struggle against the federal government. The other is that the state government wants to improve school funding without raising taxes.