The United States is the world's oldest surviving federation. Its government relies on representative democracy through a congressional system under a set of powers specified by its Constitution. However, it is "not a simple representative democracy, but a constitutional republic in which majority rule is tempered by minority rights protected by law."
There are three levels of government, consisting of the federal, state, and local levels. Officials at all three levels are either elected by voters in a secret ballot or appointed by other elected officials.
Executive and legislative offices are decided by a plurality vote of citizens in their respective districts, with judicial and cabinet-level offices nominated by the Executive branch and approved by the Legislature. In some states, judicial posts are filled by popular election rather than executive appointment.
The federal government comprises three branches, which are designed to check and balance one another's powers:
Legislative: The Congress, made up of the Senate and the House of Representatives, which makes federal law, declares war, approves treaties and has powers of impeachment.
Executive: The President, who appoints, with Senate approval, the Cabinet and other officers, who administers and enforces federal law, can veto bills, and is Commander in Chief of the military.
Judiciary: The Supreme Court and lower federal courts, whose judges are appointed by the President with Senate approval, which interpret laws and their validity under the Constitution and can overturn laws they deem unconstitutional.
The United States Congress is a bicameral legislature. The House of Representatives has 435 members, each representing a congressional district for a two-year term. House seats are apportioned among the states according to population every tenth year. Each state is guaranteed at least one representative: seven states have one each; California, the most populous state, has 53. Colorado has 7 representatives.
The second part of our bicameral Congress is the senate. Each state has two senators, elected at large to six-year terms; one third of Senate seats are up for election every second year.
American politics is dominated by the Republican Party of the United States and the Democratic Party of the United States. Members of these two parties hold the overwhelming majority of elected offices across the country at federal, state, and lower levels. Independent or so-called "third party" candidates tend to do better in lower-level elections, although there are presently some independent members of the Senate. Within American political culture the Republican Party is considered "center-right" or conservative while the Democratic Party is considered "center-left" or liberal. The size of both parties has allowed for considerable divergence of views within both parties.
Source of above: Secretary of the Senate. United States Senate Art & History: Party Division in the United States Senate, 1789 to the present.