The Constitution tries to prevent tyranny in a number of ways.
When most people think of this question, they think of the Bill of Rights. That document prevents tyrrany (they think) by listing all of the things that the government cannot do to people.
However, this is not really the way in which the Constitution prevents tyrrany. The provisions of the Bill of Rights can be overridden more or less whenever a strong majority wants to (Jim Crow, Japanese internment, Sedition Acts in WWI, preventing Mormons from practicing polygamy back in the 1800s, etc). The Bill of Rights is just words and cannot prevent the government from violating our rights.
What the Constitution really does to prevent tyranny is to set up a government with separation of powers and checks and balances. This is meant to keep the government relatively weak so that it is hard for the government to tyrannize us.
So, the Constitution's real check against tyranny is the set-up of government. It puts blocks in the way of government action so that it will be harder for tyranny to arise.
I just want to specify and add to the post above, because I believe one of the key element that, in the end, prevents tyranny, is an independent court system. When Federal judges are appointed, they are approved or rejected (almost always approved) by the Senate, and once they are approved, they are on the bench until they die or resign. They cannot be fired unless they commit a crime.
Because of this, they can rule in whichever way they see fit without worrying about losing their jobs. This allows them to rule against the government, and prevent them from going beyond their Constitutional authority. In one of the most serious cases ever to face a sitting President, the Supreme Court ruled against Richard Nixon (U.S. vs. Nixon) when he tried to argue his White House tapes were personal property. This led, in part, to the resignation of the President.
So I would argue that the court system established by the Constitution is specifically our greatest protection against tyranny.
I don't think it does. They're just words, many of which are manipulated to further a wide range of agendas. Who's gonna uphold it? If the police state doesn't respect the Constitution, who's gonna stop it?