Article V is the Constitution's instruction manual for changing itself. Amendments can be proposed by two-thirds of both houses of Congress or by a convention called at the request of two-thirds of the states, and must then be ratified by three-fourths of the states. Every one of the 27 amendments has come through the congressional route. One clause is permanently entrenched: no state can lose its equal Senate vote without its consent.
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; Provided that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.
Two steps, both hard by design. Propose: two-thirds of the House and Senate (the only route ever used), or a convention called by two-thirds of the state legislatures. Ratify: three-fourths of the states: 38 today. The President has no formal role; amendments cannot be vetoed. The Twenty-First Amendment (repealing Prohibition) is the only one ratified by state conventions instead of legislatures. The final proviso still binds: no amendment can strip a state of its equal two votes in the Senate without that state's consent.