For an overview of how the court system plays a role in making law, see my previous post.
Oklahoma has two appellate courts of ‘last resort’, one for criminal matters and one for civil matters. These courts are co-equal in authority, but differ in jurisdiction. An organizational chart can be found here. There has been little controversy over the years regarding what is a criminal matter and what is not. (For a rare example of when that boundary was tested, see Leftwich v. Court of Criminal Appeals, 2011 OK 80.)
The Oklahoma Supreme Court is responsible for all matters that are not criminal in nature. It is also responsible for administrative matters like accrediting lawyers, court reporters, etc. and occasionally issues administrative rulings in that regard. Due to the broad jurisdiction of the Supreme Court, it publishes a significant number of opinions each year. Also, in order to ease its caseload, a lesser appellate court named the Oklahoma Court of Civil Appeals handles those cases assigned to it by the Oklahoma Supreme Court.
The Oklahoma Court of Criminal Appeals is limited solely to criminal actions where the legislature has provided for an appeal. (Allen v. State, 2011 OK CR 31.) Due to the narrow scope of its jurisdiction, the Oklahoma Court of Criminal Appeals publishes far fewer cases than the Oklahoma Supreme Court.
All of these courts publish their opinions when the case should be considered binding precedent. There are vast libraries of books filled with these opinion, all maintained by private corporations who have a financial interest in having you use their books. Luckily, a few years ago Oklahoma made the decision to move from paper books as their official publisher to their own website. All of the binding precedent for Oklahoma are all online and can be searched with simple keyword searches and can be found here. To read a case citation, or to write one, it is necessary first to list the name of the plaintiff "vs." or "v." defendant followed by a comma, then the citation which is made up of the year of the decision, an abbreviation of the court, and a number which is merely how many judgments have been made that year. For example, the first case cited above was 2011 OK 80. That means that it was decided in 2011 by the Oklahoma Supreme Court and this was the 80th case of that year. The proper court abbreviations are OK for the Oklahoma Supreme Court, OK CIV APP, for the Oklahoma Court of Civil Appeals, and OK CR for the Oklahoma Court of Criminal Appeals. Most opinions, certainly all within the last ten years or so, have numbered paragraphs. This allows one to cite a particular paragraph within the opinion with the addition of "¶ (number)".