The Amendment Process
There are essentially two ways spelled out in the Constitution for how it can be amended. One has never been used.
The first method is for a bill to pass both halves of the legislature, by a two-thirds majority in each. Once the bill has passed both houses, it goes on to the states. The amendment must be approved by three-fourths of states. The bill as passed may specify whether the bill must be passed by the state legislatures or by a state convention, though the Constitution does not define a convention. This is the route taken by all current amendments. Because of some long outstanding amendments, such as the 27th, Congress will normally put a time limit (typically seven years) for the bill to be approved as an amendment.
The second method prescribed is for a Constitutional Convention to be called by two-thirds of the legislatures of the States, and for that Convention to propose one or more amendments. These amendments are then sent to the states to be approved by three-fourths of the legislatures or conventions. This route has never been taken, and there is discussion in political science circles about just how such a convention would be convened, and what kind of changes it would bring about.