John Adams appointed many judges and justices right before he left office including William Marbury.
James Madison, the Secretary of State, refused to deliver Marbury's commissions because it would validate him as a justice. Marbury took Madison to court questioning the legality of his actions.
John Marshall, the Federalist Chief Justice of the Supreme Court, led the trial and helped the court come to a ruling in favor of the federal government.
There was no dissenting opinion because the majority opinion and ruling was unanimous that withholding the commission from Marbury was illegal.
The idea of Judicial Review was established in this court case and it has been used for centuries now by the Supreme Court. Judicial Review is when the Supreme Court has the power to rule a law or an executive order to be unconstitutional.