After congress has approved a proposed amendment to the constitution, then the amendment becomes part of the constitution: an amendment becomes part of the constitution after it is proposed by two-thirds of the House of Representatives and Senate, and ratified by three-quarters of the States (which is 38 of the 50 States in USA).
Answer: After Congress has approved a proposed amendment to the Constitution
All 27 Amendments have been ratified after two-thirds of the House and Senate approve of the proposal and send it to the states for a vote. Then, three-fourths of the states must affirm the proposed Amendment.