I am confused as to how they can prevent certain kinds of speech from being used. Doesn't the Constitution say it can't be limited?
The Supreme Court does not "restrict free speech". What it does is decide whether restrictions passed by Congress, or by a state legislature, or by some regulation, executive action, or other governmental action, violate the First Amendment's guarantee of free speech.
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.
(The court has held that this was made applicable to the states via the Fourteenth Amendment. Prior to that it applied only to the Federal Government)
But the court has held that not all words are covered by this protection. It has said that obscenity is not protected speech, nor are "fighting words" nor is incitement to crime, nor is defamation. Whole books could be (and have been) written about just what is and is not protected speech under the First Amendment
But in none of these cases has the Court said what should be or will be restricted, only what could be if Congress or other legal authority chose to do so.
Justice Hugo Black famously took the view that this was absolute, that "when the first amendment said 'Congress shall make no law' it meant NO law". More formally:
Speech is wholly 'beyond the reach' of federal power to abridge ... I do not believe that any federal agencies, including Congress and the Court, have power or authority to subordinate speech and press to what they think are 'more important interests'.
But the court as a whole has never adopted Black's view. And even Black put significant limits on what he would call "speech". He did not view expressive conduct as "symbolic speech", such as flag burning or wearing a black armband.