There are actually two ways to propose an amendment stated in the Constitution and one has never been used.
In the first method a bill or project of law requires to pass both houses of the legislature by two-thirds majority in it. If the bill passes it goes on to the states. This is the way taken by all normal amendments. The second method requires a national convention to be called by two-third of the legislatures of the States and that Convention can propose one or more amendments, these amendments are sent back to the states to be approved by three-fourths of the legislatures or conventions. This method has never been taken.