Procedure
Here is a description of the steps to a civil case.

1. Filing a complaint
Any case is started by filing a complaint. The complaint is simply a document that describes (a) who you are (b) who you are suing (c) a description of why you are suing them and (d) what you expect the Court to do. After the complaint is filed, the other party is served with the complaint. Usually, they must be given the complaint in person. If it is difficult to find the other party, this can take a substantial amount of time.

2. Answering the complaint
After the other party receives the complaint, they have a limited amount of time to answer the complaint, usually 30 days. The answer states whether the other party agrees of disagrees with what you said in the complaint.

3. Discovery
During discovery, each side is allowed to discover what evidence the other party has. One party may send the other a list of questions called interrogatories. Each side may require the other to send documents that they have. Witnesses may be called to an office to answer questions before a court reporter. The court reporter writes down all the questions and the answers.

4. Motions
Either party may wish for the judge to decide on a legal issue in the case. Either party may request that the judge does this, by making a motion. For example, one party may not wish to produce evidence that the other party has requested. The party seeking disclosure would ask the judge to order the other party to produce the evidence. One party may ask the judge to dismiss the case or to grant a judgment. These requests would all be examples of motions.

5. Trial
Finally there is a trial. The case may be decided by a judge or a jury.

6. Appeal
If either party believes the judge made a mistake, they can appeal the decision to an appeals court.

During this process, the parties may agree to settle the case. This usually means that the defendant pays the plaintiff, to dismiss the case.

This process is not fast. Most cases settle without a trial. In my experience, cases usually settle about 6-12 months after they start. If a trial is necessary, the case usually takes 1-2 years. If an appeal is filed, it can take another 1-2 years.