Court rules are in place to outline the procedure through which a party goes to file a motion. Each state, county or municipality, has its own set of court rules. Occasionally, especially for motion practice, a court may have local rules regulating motion filing. Federal courts also have general rules and local rules regarding filing a motion. Typically, motions are filed with the court clerk's office, with a copy to the opposing party and judge's chamber.
There is a distinction between civil court rules and criminal court rules. The motion practice for each is very different. Civil court rules provide for mandated steps in motion-practice -- for example, the notice of hearing on the motion, the motion itself, the brief or memorandum in support of the motion, and a proof of service, indicating that the motion has been sent or delivered to the opposing party. In civil courts, a motion can be made for anything that a party determines it would like the judge to order.
As with civil practice, criminal court rules exist that outline how motions are filed. However, unlike civil motions, criminal case motions are somewhat more limited in nature. Some examples of a motion that could be filed in a criminal case are a motion to compel discovery, a motion to adjourn, a motion for a forensic mental exam, a motion for the issuance of subpoenas, and other matters listed in the court rules.
Appellate courts include state courts of appeal, state supreme courts, federal courts of appeals, the United States Supreme Court and all types of other intermediate judicial and quasi-judicial review procedures. Just like with civil courts and criminal courts, appellate courts also have their own procedural rules that govern motion practice.