In every State there are three types of courts, local (municipal, justice courts or small claims), district (county, state,) and Federal. Each court has its own rules, advantages, disadvantages and appeals procedures.
Justice Courts, also called small claims courts normally have a limit of $5,000 to $10,000 that they can award. The judge in these courts may have no legal experience or be a licensed attorney. Justice courts are designed to settle small claims and evictions. These courts are set up for unrepresented parties and do not have a court reporter. The good news about justice courts is that they are inexpensive and are automatically appeal-able de novo. De novo means all over again. There is a huge difference between de novo and appeals to an appellate court. If you decide to appeal from a county or district court to an appeals court, the appeals court will not hear the entire case all over again. They will only look at errors made by the lower court. For example, if you can prove that the lower court judge blatantly refused to follow the law or was completely arbitrary you would appeal on that basis. Therefore your task on appeal is to show why the lower court decision should be reversed based on error or abuse of discretion. This can be very challenging because you generally are not permitted to submit any additional evidence or witnesses. You may also have to post a bond if you lost in the lower court to cover the judgment and other fees. An appeal can easily take a year to reach a final decision. In many courts, you may never make an appearance but instead will file a brief explaining your position. The appealing party is called the appellant and he or she goes first and has the last word.
All states have an appeals court and then a supreme court. Generally, everyone has the right to appeal to an appeals court but not to the state's supreme court. The supreme court has the discretion to hear or refuse to hear your case.
Federal Courts are a whole different animal from state courts. Federal courts deal with civil and criminal cases and give criminal cases priority. In order to file in Federal court you must prove that you have the right to file based on jurisdiction. Jurisdiction may be found in a number of ways: litigation based on federal statutes or the Constitution, diversity of citizenship (a person from one state sues a person in another state). Federal courts have a few other distinctions from state courts. The federal rules of procedure are different but most importantly your case may be dismissed before it is even heard. For example, your opponent may move for dismissal on the basis of jurisdiction saying you don't have the right to sue in Federal court and if the court agrees, your case may be dismissed without a hearing. Of course you may submit your arguments as to why it shouldn't be dismissed but the point is you may not have your day in court. The most popular tool used to get suits dismissed early in federal court is called a 12b-6 motion which states failure to state a cause of action upon which relief may be granted. The ends and outs of these motions are beyond the scope of this blog, but a few examples of this would be that you sued the wrong person, you sued someone who is immune, or the judge is simply convinced that you haven't properly drafted your claim. All judgments from Federal court are appeal-able to the courts of appeals in the circuit covering the district court. Just like state supreme courts, the U.S. Supreme court does not have to hear your case. In fact they probably won't. I have personally been in a Federal appeals court twice and it is an enormous amount of work. The rule books are hundreds of pages long and each appeals court has their own rules that must be followed as well.
Regardless of what forum you are in, there are a few blogs that you must have, most of which are all online: Rules of Civil Procedure, Rules of Evidence, Local court rules, and some way to research your case like Findlaw.com.