Really, you don't. At least not a constitutional right.
The Constitution of the United States was ratified in 1789, but it doesn't guarantee you the right to vote. The earliest known code of justice, found in Iraq (Sumeria), dates back to about 2300 BC. Aristotle, in 350 BC, was the first to draw a distinction between law and constitutional law. But today state law is used to determine your qualification to vote, and your rights vary considerably depending on where you live.
Constitutional amendments have been made over the years to make sure certain voting rights are available to all citizens.
The 15th amendment provides that you cannot be denied the right to vote because of your race or gender. In 1960, citizens in Washington DC--which isn't a state, but at the time had a greater population than 13 of the 50 states--were allowed to vote for President. The 26th amendment gives 18-year-olds the right to vote. You can vote even if you can't afford to pay a poll tax thanks to the 24th amendment. But the Constitution never explicitly ensures your right to vote.
In fact, your right to vote can be withheld by state law as long as the law doesn't conflict with anything in the Constitution. For example, in Texas if you're mentally incompetent or a felon you can't vote.
On the other hand, states can allow persons younger than 18 to vote. In 2004 a bill that would have allowed anyone 14 or older to vote passed the California Senate Committee on Elections and Reappointment, but was never enacted.
So if you're 18 or older and not in a Texas jail, go vote today!