If you are convicted of driving under the influence (DUI) by a trial court, you still have a right to appeal the court's finding to an appeal (sometimes called appellate) court. This appeal is not automatic. Appellate courts are very strict about when appeals are filed, and the exact details and requirements vary state to state. There is a set period of time within which to file an appeal (often 30 days), and if the appeal is filed even a day late, it will be rejected. You should also know that if you pleaded guilty, there is a much smaller chance of being successful on appeal than if you were found guilty after a trial.
An appeal is very different from a trial. If your trial lawyer does not have experience with appeals, it may be worthwhile to retain an appellate lawyer to handle the appeal. An appeal is not a new trial. A trial court determines the facts of the case and applies the law to them. The appellate court, often a panel of three judges, reviews the prior trial for legal errors by the trial judge. If you and your attorney disagree with a fact that the court found at trial, this will not be overturned on appeal. Only legal issues such as the trial court's application of the proper laws, or rulings on admission of evidence, will be considered by the appellate court.
The transcript of the trial is sent to the appellate court for review. Your attorney will then file a brief, which tells how the trial court made mistakes and where in the transcript they can be found. The opposing party that prosecuted the case, usually the State, next files a brief that explains why they believe the trial court's decision was correct and should be upheld. Your attorney will then file a reply brief, wherein she can respond to the State's arguments. You should ask your attorney to provide you with copies of all briefs filed during your appeal. After the briefs have been filed, the appellate court may ask both attorneys to appear and present brief oral arguments in support of their positions. This is not always required. Even though the time to file an appeal is short, the time an appellate court takes to decide appeals can take several months. The appellate court can deny the appeal, which means the trial court's verdict is approved. If the appellate court reverses the trial court, this means the verdict is thrown out. The appellate court can then either dismiss the case against you, or remand (which means send it back) to the trial court with instructions on how to correct any errors. In most DUI cases, the court proceedings end after this first appeal. Appeals to a higher court such as a state supreme court are very rare, because most of the time the appellate court must agree that your case is worthwhile and should be appealed again. This does not happen often, but when it does, the process is similar to the first appeal.