Judicial opportunities generally fall into two categories: clerkships and internships. 
Judicial internships are part-time, volunteer positions for law students that provide an opportunity for students to gain first-hand experience with judicial procedure.  Interns generally are supervised by judicial law clerks and assist the law clerks with research and writing assignments.  A judicial internship can be an important steppingstone to obtaining a judicial clerkship.
Judicial law clerkships generally are 1-2 year, full-time, paid positions open to recent law school graduates and new attorneys.  Law clerks provide direct counsel and assistance to a judge by reviewing case records and filings; conducting legal research; preparing bench memos and orders; and drafting opinions.  As noted above, many law clerks also supervise judicial interns.
Many federal court judges participate in the federal clerk hiring law plan, which centralizes applications in the Online System for Clerkship Application and Review (OSCAR).  However, not all judges advertise judicial clerkship and internship positions, on OSCAR, so [Note about OSCAR – not all judicial opportunities are on Oscar, so be sure to check the webpages of the courts and other job posting sites (e.g., Symplicity) to avoid missing any potential judicial opportunities.
Note that U.S. citizenship is required for paid positions in the U.S. Courts.  Some unpaid positions may be open to non-U.S. citizens.  Carefully review the requirements for each position prior to submitting an application.
In the United States, two courts, the United States Court of International Trade and the United States Court of Appeals for the Federal Circuit, have jurisdiction over international trade matters.
Courts and Judicial Programs

U.S. Court of International Trade

U.S. Court of Appeals for the Federal Circuit

Judicial Resources Committee of the United States Judicial Conference and Just the Beginning - Pipeline Organization