First off, know what to expect. You have a right to a court-appointed defender, an attorney, or self defense (representing yourself in court). A lawyer is always recommended. He or she will explain the proceedings to you from the get go; make sure you listen and follow their advice. They will guide you through the entire process.
Make sure you do your research before hand. For research regarding DUIs, you can use the internet or public libraries. While asking people you know for information is also research, make sure they are well versed on the topic. It is important for you to know the consequences of your actions, both at the time of the arrest and during the hearing. A DUI is a very serious crime with very serious implications, make sure you know your state's DUI laws before heading to court.
Once you have been arrested and have a lawyer, the first step in the court proceedings is known as the arraignment. It is during this first court hearing where you will plead Guilty, or Not Guilty. Once you have pleaded, it is your lawyers' job to plead your case from this point onward.