If we are talking about the original US Constitution, not including the Bill of Rights or any other amendments, the answer is that it protected American liberties in two ways.
First, the Constitution protected American liberties by specifically guaranteeing a few of them. It did not guarantee things like the freedom of speech, but it did guarantee a few rights. For example, it guaranteed the right to writs of habeas corpus. It guaranteed that government could not make ex post facto laws, prosecuting people for things that were legal when they were done. It guaranteed that government could not pass bills of attainder, declaring people guilty of crimes simply by an act of the legislature. All of these were specific guarantees of American liberties in the Constitution.
Perhaps more importantly, though, the Constitution protected American liberty by setting up a system of separation of powers and checks and balances. By doing this, the Constitution made it much harder for the government to take away the people’s liberties. In order to take people’s liberties away, the government would have to gain the approval of two different houses of Congress, a president elected separately, and a Supreme Court that was not elected. Therefore, no one person or one part of government could easily take power and threaten the people’s liberties. By setting up a government that would not find it easy to take controversial actions, the Constitution protected American liberty.