Article III creates the Supreme Court and lets Congress build the lower federal courts. Federal judges serve during "good Behaviour", effectively for life, with salaries that cannot be cut, insulating them from political retaliation. The article defines which cases federal courts may hear, guarantees jury trials for federal crimes, and defines treason so narrowly that the charge cannot become a political weapon. Judicial review, courts striking down unconstitutional laws, is not stated here; the Supreme Court claimed it in Marbury v. Madison (1803).
The judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish. The Judges, both of the supreme and inferior Courts, shall hold their Offices during good Behaviour, and shall, at stated Times, receive for their Services, a Compensation, which shall not be diminished during their Continuance in Office.
The Constitution requires exactly one court, the Supreme Court, and leaves the rest to Congress, which created the district and circuit courts you can explore on the Courts pages. Even the Supreme Court's size is set by statute, not the Constitution. Judges serve for life unless impeached, and their pay can never be cut, so neither Congress nor the President can punish a court for its rulings.
The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, and Treaties made, or which shall be made, under their Authority;—to all Cases affecting Ambassadors, other public Ministers and Consuls;—to all Cases of admiralty and maritime Jurisdiction;—to Controversies to which the United States shall be a Party;—to Controversies between two or more States;— between a State and Citizens of another State,—between Citizens of different States,—between Citizens of the same State claiming Lands under Grants of different States, and between a State, or the Citizens thereof, and foreign States, Citizens or Subjects.
In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.
The Trial of all Crimes, except in Cases of Impeachment, shall be by Jury; and such Trial shall be held in the State where the said Crimes shall have been committed; but when not committed within any State, the Trial shall be at such Place or Places as the Congress may by Law have directed.
Federal courts hear "cases and controversies", real disputes, not abstract questions, arising under the Constitution, federal law, and treaties, plus disputes between states, between citizens of different states, and cases involving the United States itself. The Supreme Court starts as the trial court only in a sliver of cases (states suing states, ambassador cases); everything else reaches it on appeal, under rules Congress sets. Every federal criminal trial is by jury, held in the state where the crime occurred. The Eleventh Amendment later narrowed federal courts' power to hear suits against a state by citizens of another state.
Treason against the United States, shall consist only in levying War against them, or in adhering to their Enemies, giving them Aid and Comfort. No Person shall be convicted of Treason unless on the Testimony of two Witnesses to the same overt Act, or on Confession in open Court.
The Congress shall have Power to declare the Punishment of Treason, but no Attainder of Treason shall work Corruption of Blood, or Forfeiture except during the Life of the Person attainted.
The only crime the Constitution defines, and it defines it narrowly on purpose: only making war on the United States or aiding its enemies counts, and conviction requires two witnesses to the same overt act or a confession in open court. In England, "treason" had been stretched to punish political dissent; the framers made that impossible here. Punishment cannot extend to the traitor's family ("corruption of blood").