Two routes for proposing amendments
Article V allows proposals by two-thirds majorities in each chamber of Congress or by a convention called by Congress on the applications of two-thirds of state legislatures. These are proposal requirements, not thresholds that by themselves change the Constitution.
Congress uses a joint resolution to propose an amendment. The National Archives explains that the President has no constitutional approval role in this amendment procedure and that the resolution is not sent to the White House for signature, unlike ordinary legislation.
Ratification and a protected state interest
A proposal must then be ratified by legislatures or conventions in three-fourths of the states, using the mode specified by Congress. Ratifying conventions belong to a different stage from a convention that proposes amendments, even though both are called conventions.
Article V also prevents a state from being deprived of its equal suffrage in the Senate without its consent. Its original text contains additional restrictions expressly limited to the period before 1808. Those expired temporal conditions should be distinguished from the equal-suffrage protection.
References: [1]
Ratification, effectiveness and the documentary record
After ratification, states send official or certified records to the National Archives. The Office of the Federal Register examines facial legal sufficiency and authenticating signatures and preserves the records. Certification provides official notice of completion; record administration does not replace state ratification.
Congress proposed twelve amendments together in 1789. Ten were ratified in 1791 as the Bill of Rights; another proposal about congressional compensation became the Twenty-Seventh Amendment in 1992. Proposal dates, ratification dates and the numbering of adopted amendments are therefore distinct pieces of information.