To propose and ratify formal amendments to the Constitution, there are four different methods by which these formal amendments may follow. One method is that a formal amendment may be proposed by each house of Congress by a 2/3 vote. The formal amendment is ratified through this process with a ¾ vote by the state legislature. A second method for formal amendments is to have Congress propose the amendment, and then to have the amendment ratified by conventions which are called strictly for the purpose of that amendment in ¾ of the states. A state convention is different from state legislature, and because of this, the political nature of a convention is different. This is an unusual way to formalize an amendment.
A third method for proposing and ratifying an amendment is to have the amendment proposed at a national convention which is called for by Congress, which is called strictly for the purpose of the proposal by 2/3 of state legislatures. The amendment is ratified when ¾ of state legislatures vote and approve the new amendment. The fourth way to get a new amendment proposed and ratified is that the amendment can be proposed by a national convention, not Congress, and then it is ratified with ¾ of the states having conventions that approve the amendment.
The most common way that an amendment is proposed and ratified is the first method of having the amendment proposed by each house of Congress in a 2/3 vote, and then ratified by ¾ of the state legislatures. Through this process, each house of Congress is involved, and the amendment stays in the political arena of Congress and legislatures. The less common ways of proposing and ratifying amendments are through conventions that in a sense circumvent Congress and state legislatures by changing the political nature of the vote.