There are two kinds of municipal court in Oklahoma and they are distinguished from each other by the population of their municipalities. If the population is large enough then the court is a "court of record" which essentially means that its convictions count against you in the future since an official record is kept. The other kind is a court "not of record" and since it doesn't keep official records its ability to punish a defendant is more limited.
What Happens in a Municipal Court of Record
Oklahoma City and Tulsa are the municipal courts of record; the rest are not. When you get arrested and a city with a court of record elects to prosecute you (the state declines or never hears about the offense) then you have hearings and a trial. The result of the trial can be appealed to the Court of Criminal Appeals, which is like Oklahoma's supreme court for crime (we also have a Supreme Court, but it doesn't have much to do with criminal appeals other than to reject them and send them to the Court of Criminal Appeals). The Court of Criminal Appeals will review the record and rule on any complaints raised in the appeal.
What Happens in a Municipal Court Not of Record
The other municipal courts (Norman, for example) have a similar procedure but generally do not keep a transcript of the trials or other real records other than the judgement which is not published broadly. In such courts a defendant who wishes to appeal the result has a different path than the Court of Criminal Appeals initially. First, they file a Notice of Appeal with the Municipal Court and then they file their appeal in the District Court (County Court) in the County wherein the municipal court sits (so for Norman, Cleveland County, and for Bethany, Oklahoma County). The District Court then holds a trial de novo; a whole new trial where the new judge and possibly a new jury will decide on the guilt or innocence of the accused with the new ruling replacing the old ruling entirely. Because District Courts are of record a court reporter is available (but make sure he or she is gonna be present, this usually involves a fee) and the result of the trial de novo can then be appealed to the Court of Criminal Appeals.
Things to Consider
The upside of having a case in a municipal court not of record is that you can have an extra bite at the apple so to speak. The downside of the trial de novo is that if you're found guilty again you're in a court of record so there is a record. I generally think it's better for most people not to have a record. Consider carefully whether you want to make a record before appealing your case from a court not of record to the District Court. It can be worth it if the municipal court is clearly prosecuting things that aren't crimes for example, but if you're guilty it might be better not to memorialize it.
If you want to fight your charges in municipal court call a criminal defense lawyer at (405) 310-9890 for a free consultation.