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.