describe the formal amendment process that has been used most often to formally amend the constitution

The formal amendment process that has been used the most often to reform the Constitution is the Congressional Method:

1) Two thirds of the present members of the House of Representatives and the Senate proposse and amendment.

2) The amendment has to be ratified by three-fourths of the Legislatures of the States.

There are also less used methods both for propossing an amendment and for ratifying it: The Convention Method

In this method, the amendment is propossed by two thirds of the members of a National Convention which is formed by order of the Congress after the petition of three-fourths of the legislatures of the states.

The ratification can be achieved also by the approval of three-fourths of the ratifying conventions in each state.