What substantive and procedural law is applied by a judge in a federal or state court?

Answer 1

This information is for civil cases:
The federal courts use basically federal procedural and substantive law. The state courts use state procedural and substantive law. When there is a conflict of law situation, one party from one jurisdiction and another from another things can get complicated. Contact a lawyer.
In criminal cases there is not so many conflict of law problems.

Answer 2

It depends upon the type of case and the court.

Federal:
In a case interpreting federal law, the Federal Rules of Civil Procedure control the procedural law, and the substantive law is the law being interpreted.

In a case based on diversity jurisdiction, the Federal Rules of Civil Procedure cover some aspects of the case, while the law of the state in which the case is brought controls both substantive and some procedural issues (such as statutes of limitation).

One exception: in a diversity case, if there is a contract which specifies that the law of a particular state or jurisdiction applies, ordinarily, such a clause would be honored.

State:
The judge applies the law of the state, substantive and procedural, with one exception: if there is a contract which specifies that the law of a particular state or jurisdiction applies, ordinarily, such a clause would be honored.

Answer 3

David B. has got it right.