Article V of the United States Constitution describes the process whereby the Constitution may be altered.  Altering the Constitution consists of proposing an amendment or amendments and subsequent ratification.

Amendments may be adopted and sent to the states for ratification by either:

• Two-thirds (supermajority) of both the Senate and the House of Representatives of the United States Congress, OR
• By a national convention assembled at the request of the legislatures of at least two-thirds (at present 34) of the states. 

To become part of the Constitution, an amendment (as determined by Congress)  must be ratified by either:

• The request of Legislatures of three-fourths (at present 38) of the states; OR
• State ratifying conventions in three-fourths (at present 38) of the states.

Source: Wikipedia

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Writing extensively about the amendment process in Federalist No. 85*, Alexander Hamilton makes clear that Article V allows the states to hold the federal government accountable by allowing them to call an amending convention and propose specific amendments: “But every amendment to the Constitution, if once established, would be a single proposition, and might be brought forward singly...There can, therefore, be no comparison between the facility of affecting an amendment, and that of establishing in the first instance a complete Constitution. We may safely rely on the disposition of the State Legislatures to erect barriers against the encroachments of the national authority.”

For further information on Federalist No. 85:  http://www.teaparty911.com/info/federalist-papers/no85.htm

Source: Senator David Long "Amending the U.S. Constitution by State-Led Convention"