Article V of the Constitution stipulates how the Constitution is to be amended. There are two steps to constitutional amendment: proposal and ratification. At the proposal stage, you can do it one of two ways: either have Congress pass a joint resolution with a 2/3 vote in both houses or 2/3 of the state legislatures can request that Congress call for a national convention (a convention similar to the one that created the Constitution in the first place). This second method of proposal has never been used.
Once a proposal has been passed, it needs to be ratified. Again, there are two ways to do this. One way is for 3/4 of the state legislatures to pass the proposal by majority vote. The second method is for 3/4 of the state legislatures to call a convention to ratify the amendment. This second method of ratification has only ever been used one: with the repeal of prohibition.
The Constitution has been amended at 18 different times. The first ten amendments to the Constitution were passed all at once. We call these collectively the Bill of Rights. The last amendment to the Constitution, the 27th Amendment, was ratified in 1992. That amendment, having to do with congressional pay, stipulates that a pay raise for members of Congress cannot take effect until after the next congressional election.