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The United States of America has a "federal" system of government. Power is distributed between the individual states and the national (federal) government. We also have a distribution of power between three "branches" of government: the executive branch which carries out the laws, the legislative branch which writes the laws, and the judicial branch which decides controversies including how to apply the laws to specific situations. The United States is a Republic, in which the people elect representatives to make the laws for them. Each state is also required to have a republican form of government.

The President of the United States is head of the federal executive branch. He is elected every four years through the "electoral college." No, that's not a university. It's actually a group of people elected by the voters of each state to in turn vote for who the President shall be. But you probably won't see the name of electors on your ballot. Instead, you see the name of the Presidential candidate to which the electors are pledged, so to speak. When you vote for a presidential candidate, you vote for the electors pledged to that candidate. The number of electoral votes each state gets is determined, in part, by state population. More populous states get more electoral votes than less populous states.

The federal legislature is Congress. It consists of two "chambers": the House of Representatives and the Senate. Each state elects two senators. Senators serve six-year terms, but the terms are staggered so that not all the senators are elected in the same year. Part of the Senate is elected every two years. The members of the House of Representatives. All the House positions are subject to election in the same year. Each state has at least one member in the House, but the higher a state's population is, the more Representatives is gets in the House. Most states are divided into Congressional Districts, so that each House member from that state is elected by voters from a specific region of the state. For a bill to become law, it must be passed by both the House and the Senate. Then the President can either sign or veto it. If he signs it after it has passed Congress, it becomes law. If he vetoes it, the House and Senate can make it law without his signature by passing it again with a super-majority vote. 

Federal judges are appointed by the President, subject to confirmation by the Senate. They serve basically for life, although they can resign or be impeached.

Do you want to know more about U.S. government? Why don't you read the U.S. Constitution?

The U.S. Constitution can be found HERE (external link).