So you've just registered your copyright for your new song, and days later you hear it on the radio without your permission! In order to protect your rights you obtain an injunction and sue for monetary damages. An injunction is a remedy in the form of a court order that prohibits a party from doing certain acts. In our case, the people who copied your song is the other party and the "certain acts" are copying your music.
Copyright is a federal issue, and as such all cases are tried in the US District Court. Each state has at least one of these courts. Assuming that your work is registered with the US Copyright Office, proving your ownership of the copyrighted material will be a cake walk. The difficulty comes in proving the defendant copied it in the first place. Courts do not require direct proof of copying to declare infringement. You must prove that the defendant had access to your work and that his or her work is replicated as a result of this access. On the other hand, if your opponent can prove that he did not have access to your work then he is not liable for copyright infringement, even if his work is a direct replica of your own. If in our example we had performed our song in public, then the court would find the defendant guilty of infringement due to a "reasonable opportunity to view the work."
Before the case even begins, you can file for a preliminary injunction. This will prevent the defendant from producing further copies of the work during the trial. A down payment will usually be required, however, in the instance that the defendant is found not guilty and damages are brought. A preliminary injunction becomes a permanent injunction after the defendant is found guilty.
Money damages are another remedy to copyright infringement. If the court decides in your favor then you are entiltled to not only your actual damages but any profit that the defendent made as well. The determining factor of your actual damages lies in whether or not your work suffered in market value due to the infringment. Proof of actual damages is difficult, so federal law provides statutory damages of $500 to $20,000 per act of infringement.