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Like the governments of the federated states, the federal government of the US (also called the national government or the central government) consists of three branches, which correspond to the three major functions of government identified by political philosophers: the legislative, the executive and the judicial. The general outline of the federal government is described in the US Constitution. (Some of my thoughts about the Constitution can be found here. Read the Constitution and some official comments on it at the US National Archives site, here.)
Though the general structure of the government is familiar, since it is common to many other countries and states, the mechanisms of its internal functioning are specific to the situation in the US, at the time the Constitution was written, and necessarily today as well. In particular, the organization of Congress and the election of the President both reflect the importance of the states, that is, the federal government is itself an example of the principle of federalism in action.
The legislative branch, Congress (the Senate and the House of Representatives)
The executive branch, the President, the Presidency, the Electoral College and Presidential elections; removal from office: impeachment.
The judicial branch, including the Supreme Court
Some of the compromises that were included in the Constitution.