A constitutional amendment is proposed by Congress with the House of Representatives and Senate supporting the motion with a two-thirds majority vote. It is also proposed by a constitutional convention of two-thirds of the state legislators. There is no record of the latter ever occurring in American history.
The process for proposing a constitutional amendment is started in Congress or through a motion by a majority of state legislators. It starts by writing a proposal called a joint resolution that states why the amendment is needed and why the existing constitution is not presently able to meet this demand.
Once the new bill is proposed, it is reviewed first in the House of Representatives and then the Senate. It must receive two-thirds majority voting support to move from the first location to the next. There also is a set period of time between these intervals that must be met. When bills are allowed to remain outstanding longer than this period, they are automatically dismissed.
There is no record of a constitutional convention ever being hosted in the history of the nation. This function is available in the event it is needed, but is unlikely to occur because of the division found in legislative groups between states.