How are amendments to the US constitution ratified?

Amendments to the US Constitution are proposed and ratified according to the process listed in Article 5 of the Constitution, typically passage of the amendment by a 2/3 vote of both houses of Congress, followed by ratification by state legislatures in at least 3/4 of the individual states.

A second process for proposal (never successfully completed) is by a national convention called by 2/3 of the individual states.

A second process for ratification (used for the 21st Amendment in 1933) is by state conventions rather than state legislatures.