The best known way in which the Federalist tried to do this was through the appointment of the "midnight judges" that led to the Supreme Court case of Marbury v. Madison. They also did a couple of other things having to do with the judicial branch.
After being voted out of office, Pres. John Adams tried to increase the number of Federalist judges in important positions. To do this, he appointed 16 new judges as federal circuit judges and he appointed 50 other men as justices of the peace for the District of Columbia. In addition to doing this, Adams appointed his own Secretary of State, a man named John Marshall, to be the new Chief Justice of the Supreme Court. Finally, Congress reduced the size of the Supreme Court from 6 to 5, effective with the next vacancy. This would preven Jefferson from appointing a successor to the next Justice who left the Court.
In these ways, the Federalists tried to keep control of the judicial branch after they were voted out of office in 1800.