There's not much substantive or procedural law in the Constitution for how trials are held. The Constitution is a list of enumerated powers - what the three branches are allowed to do.
Article III does allow Congress to create federal courts.
Trial procedure was all brought in at the state level from each state's common law which evolved from English common law, and at the federal level, through Congressional statute (the Judiciary Act of 1789 and the Federal Rules of Procedure, first adopted in 1937).