There are two ways to propose an amendment to the U.S. Constitution today:
1. A vote of a two-thirds majority in both the House of Representatives and the Senate.
2. A vote of two-thirds of the state legislatures calling for Congress to call a national convention to propose amendment.
There are also two ways to ratify an amendment to the Constitution:
1. By legislatures in three-fourths of the states.
2. By conventions in three-fourths of the states.
So far the method of proposal used has always been the two-thirds vote in Congress. The other one has never been used because it is more difficult and time-consuming. The method of ratification that has been used most is the one which requires the vote of three-fourths of the state legislatures, on all but one of the 27 amendments. The other one has only been used once, on the 21st amendment.
That is the formal method of amending the Constitution. There is also an informal method. Judicial interpretation and cultural and social change also have had a major impact on how we interpret the Constitution. An example of judicial interpretation informally amending the Constitution is the court case Roe v Wade, which made abortion legal. An example of social and cultural change informally amending the Constitution can be seen in the type of content in entertainment these days. 50 years ago, you would never see any explicit violence on TV; today it is the norm.
That is how Constitutional amendments have been passed and are still passed in the United States today.