The founding fathers recognized that Congress could become a choke point of progress. Much like many of the states have methods for citizens to bypass the legislative branch, our constitution provides a method for the states to bypass the federal government.

Article V of the current US Constitution:

"The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress; Provided that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate."

To summarize: a constitutional convention MUST be called by Congress when two-thirds of the state legislatures apply to (petition) the US Congress for a convention. Some read this to imply that the legislatures must sponsor a specific amendment. Since Article V says "shall call a Convention for proposing Amendments" (note the plural "Amendments"), I read this to mean that two-thirds of the state legislatures (34 or more, currently) must simply request a convention to consider any and all proposed amendments.

As a practical matter, it is unlikely that a state legislature would petition for a convention without a considered reason - a specific amendment, not a general "we need to fix the Constitution" concept. However, once the convention is called, whatever brought the state to the meeting must be considered by the group.

How would such a convention be organized? This is not at all clear. Most probably like the original convention - each state would send a team of representatives to be certain that their reason for being at the meeting was handled appropriately. I view this to imply that the states' representatives would prepare a set of proposed amendments which would be presented to each of the states. If three-fourths of the state legislatures (or - if Congress decides as provided by Article V - conventions from within the states convened for the purpose of reviewing the proposals) approve the proposed amendment, it becomes part of the Constitution.

A concise review of this process can be read at:

http://www.lessonplanspage.com/SSInfoDiscAct-DoWeNeedANewConstConvention912.htm