Article V of the Constitution states:
The Congress, whenever two thirds of both Houses shall deem it
necessary, shall propose Amendments to this Constitution, or, on
the Application of the Legislatures of two thirds of the several
States, shall call a Convention for proposing Amendments, which, in
either Case, shall be valid to all Intents and Purposes, as part of
this Constitution, when ratified by the Legislatures of three
fourths of the several States, or by Conventions in three fourths
thereof, as the one or the other Mode of Ratification may be
proposed by the Congress
So an amendment can become part of the Constitution either:
1) By the passage of the amendment by 2/3 of the house and 2/3
of the senate, followed by ratification by the legislatures of 3/4
of the states.
OR
2) By the legislatures of 2/3 of the states calling a special
convention where any approved amendments must be followed by
ratification by the legislatures of 3/4 of all the states.
Only the first method has ever been successfully used to amend
the US Constitution.