I undertand that there are 27 Amendments to the US Constitution. But how does the US amend the Constitution?

Article V of the Constitution describes how to amend the Constitution.  There are two ways.

Method I:    First, 2/3 of the House of Representatives and the Senate must approve the amendment.  Then, 3/4 of the states’ legislatures must approve the amendment.  

Method II: 2/3 of the states call for a special convention to propose the amendment.  Then, 3/4 of the states’ legislatures must approve the amendment.  This method has never been used.