Here is the basic outline, with a link to the actual law’s text, if you need it: http://www.fjc.gov/history/home.nsf/page/landmark_02.html
The Judiciary Act of 1789 was the very first bill considered by the very first Congress under the Constitution. Antifederalists opposed this bill because they believed that a federal court system would deprive state courts of their own powers and privileges.
The Judiciary Act of 1789 established a three tier federal court system. There were thirteen district courts, and three circuit courts to which appeals could be made. From the circuit courts, appeals could be made to the Supreme Court. Supreme Court justices were required to also serve as circuit court justices, riding a circuit from town to town and therefore supposedly being more in touch with the common people. The Act also established the number of justices on the US Supreme Court at six. There was one chief justice and five associate justices. The fact that this was an even number made it possible to have tie votes as a common occurrence. (As more states were added to the union, more district courts and Supreme Court justices were added until, by the time of the Civil War, there were 10 justices total on the US Supreme Court. In 1866, Congress reduced the number to 7, and in 1869 it was raised to 9, which is pretty much where it has remained ever since. Just remember that nothing in the Constitution itself specifies the number of justices or courts and judges that there must be at the federal level. The Act limited US Supreme Court jurisdiction to hearing appeals from the lower federal court and to judge the constitutionality of state supreme court decisions or over disputes between states.
The Judiciary Act also established the office of Attorney General, whose primary job back then was to provide legal advise to the president. The attorney general then joined the three secretaries of War, State, and Treasury in the cabinet.