The first questions you need to ask is whether your case is appropriate for an appeal. Generally, your case would have proceeded to trial and a judgment was issued by the judge if you are looking to pursue an appeal. There are rare circumstances where settled cases are appealed, but those are few and far between. If the case was tried, then the post-trial motions must have been ruled on and the case must have become final. Once the case is final, you have 10 days to file an appeal.
If you are interested in filing an appeal, then the first step would be discussing it with the attorney who represented you at trial. However, if you are considering an appeal, then you are likely not happy with the results and may choose to consult with a different attorney. Some trial attorneys also do not handle appeals, which would force you to consult a different attorney. Either way, consult your current attorney or a new attorney as soon as possible.
Once you figure out who will represent you, either you or your attorney needs to file all of the appropriate paperwork with the Circuit Court where the case was tried. Make sure not to miss the 10 day deadline. You will also need to order copies of the transcript from the case and the legal file and file those with the Court of Appeals.
Appeals can be a very tricky process, so it is important to follow the requirements closely and prepare well in advance to proceed to the Court of Appeals.