What amendment says that powers not given to the federal government by the Constitution belong to the states or to the people?
The Tenth Amendment says this. Specifically, it says that
...powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.
Like the rest of the Bill of Rights, the Tenth Amendment addressed some of the concerns of Anti-Federalists, people who had raised concerns about the new Constitution, largely on the grounds that it contained insufficient protections for the political powers of the states and the people. They worried that a broad interpretation of clauses related to elections, taxation, the military, and other issues would weaken the states at the expense of the federal government. The Tenth Amendment was intended to protect against these kinds of abuses by clearly defining the system of federalism set up by the Constitution. All powers not expressly delegated to the federal government would be retained by the states. Over time, multiple Supreme Court cases have arisen involving the Tenth Amendment, including McCulloch v. Maryland, Gibbons v. Ogden, and many others--indeed any cases that involve the states rights against the powers of the federal government. Some of the powers claimed by the states under the Tenth Amendment include licensing, regulating education, and many others.