There are two ways to amend the Constitution
well 3
First is most common: 5 guys on the Supreme Court "clarify" the constitution. Like when they ordered states' power for racial segregation, and mandatory sterilization of the mentally ill; and took it back; and guaranteed abortion; and took away the death penalty, and brought it back; and banned race-based setasides, and brought them back; and outlawed execution of the mentally ill, and adults who killed people deliberately before their 18th birthday; and allowed states to take private property and give it to another owner; and allowed criminalization of political ads, and took it back.
with that crap said
The first LEGIT way to amend the constitution is for Congress to pass the proposed Amendment, both House and Senate, and refer it to the States for ratification, and if 3/4 ratify it, it becomes amendment.
the Second legit way is for 3/4 of state legislatures to pass a call for convention. And then they send delegates of their choosing to the convention. And the President and the Senate and the House get to read about it in the paper 
the reason that hasn't been tried in 200 years is that the old states under the articles of confederation called a convention to suggest reforms, and the convention decided to scrap the Articles and come up with a whole new government. The states got to vote on whether or not to accept it, but a constitutional convention answers to nobody.
It's getting to the point where that would make more sense than voting on either Democrats or Republicans to solve our problems :s
But the main selling point for the states is "unfunded mandates". Where Congress says "states, if you want any money from us at all, thou shalt have little yellow schoolbuses for disabled kids. And girls sports get as much money as guys sports. and your speed limit is what we tell you. And you gotta monitor workplace safety. And regulate smog. And traffic. And now, you gotta tear up whatever insurance code you have, and enact A-Z inclusive excluding P and Q. etc"
And the states say "OK how much do we get paid to do all that?" and Congress says "nothing muhahahaha"
and the states say "that's not how the constitution meant it to work" and Congress gets all hoarse and says "I have altered the deal pray I don't alter it further"
Democrats think we can have all sorts of national goodness and spare the federal budget by ordering states to pay for administration and the states are about fed up with it, finally. Ya can't hustle a hustler and they didn't hack their way into state office just to be a bitch for Pimp Pelosi.
The core joke of Hitchhiker's Guide to the Galaxy is that of course no civilization would develop personal computers with instant remote database recovery, and then waste this technology to find good drinks.
Steve Jobs has ruined this joke.