Article V
Section I
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.
Full text taken from the US government transcript site.
the meaning of Article V.
This article is all about the Constitution itself. This shows how great the founders were at this whole government business. They realized that there would be times in the future when it would be necessary to fine tune how the government works or to address some forgotten point. In fact, they KNEW there was going to be additional items added becuase part of the deal made at the convention and during the debates afterward was to Amend the US Constitution with a Bill of Rights to add extra protections for individual rights. Not bad for a bunch of farmers and rebels! As always, I highly recomend reading the original language at the government archive site either before or after reading my explanation. It would be a good idea to read the Federalist and Anti-Federalist papers as well as James Madison's notes on the Constitutional Convention if you want to understand what the founding fathers were so worried about. The Bill of Rights in particular would never have happened without the Federalist and Anti-Federalist discussions. How about that? The Constitution gets a tune-up once in a while!
Section I
Like I said above, this is all about fixing the Constitution if and when it breaks in some way. There is always something you didn't think of that someone else might have. That is what Amendments are for, fixing those spots that you didn't think of or things that have changed over time.
There are two ways to officially and legally change the US Constitution. The first is for Congress to pass an Amendment bill through both the Senate and the House of Representatives with a two thirds (2/3) majority. Once the Amendment has passed both then it is sent on to the states to be "Ratified" which means that the state legislatures vote to to allow the amendment to be added to the Constitution. 
The second way to make a change is for the state Legislatures of two thirds (2/3) of the states vote to hold another Constitutional Convention. If a Convention is held then the delegates discuss proposed amendments and send them to the states after a three fourths majority voe (3/4) for approval or rejection.
In both of the options for changing our Constitution the same end vote must be taken by the state Legislatures. Each state will review the proposed Amendments and then hold a vote. If three fourths of the state Legislatures approve the amendment it is passed into law and added to the end of the Constitution. Some Amendments waited many years to finally be ratified, the 27th took 200 years! Now when Congress proposes an Amendment they put a time limit on when it can be approved. Approval can be by the regular Legislature or by a Convention of Delegates held in each state, the voting majority still has to three fourths (3/4).
The President of the United States has no say in whether an Amendment passes or is rejected. The whole process is handled without the President.
This article also specifies a part of the Constitution that cannot be changed by the Amendment. process. The forbidden change has to do with equal representation for the states. It really means that no state can be deprived of their representation in the federal government. This is to keep the larger states from changing the rules to keep the smaller states out of the game.
Section II
Just kidding...this Article only has one section!
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