Question

What is the most common process used in amending the constitution ​

Answer 1

The most common method used to add amendments to the Constitution is the first method.  An Amendment may be proposed by two- thirds vote in each House of Congress and ratified by three- fourths of State Legislators.

Article 5 gives the process of amending the US Constitution.  Both the Senate and the House of Representatives, in the US Congress, approve by a 2/3 majority voting.  This is a joint resolution that amends the Constitution.  By this the President's signature is not required.