The defendant can appeal a finding of guilt after most convictions. Appeals in criminal cases are rarely successful (on the order of 10%) and are based on errors of law. The appellate court will not determine if the jury was "right" or "wrong", and you will not succeed on an appeal simply because you don't like the result. Appeals are only granted where a legal error was committed during the process. Examples of a legal error: the prosecutor engages in misconduct during final argument, or the judge reads an improper instruction to the jury. The appellate court will typically not consider changing whatever facts were determined by the fact finder at trial (usually the jury), they will accept these facts as proven and look only for errors of law. The law guarantees you a fair trial with all due process, but it does not guarantee you what facts will be proven and the appellate court will not typically disturb any findings of fact. The best way to avoid having to appeal, of course, is to avoid a conviction in the first place.
Not all criminal trial lawyers handle criminal appeals. Appellate law is a focus of appellate lawyers who may or may not also do trial work. Don't be surprised if your trial lawyer refers you to another lawyer to handle your appeal. It doesn't mean he doesn't have hope or want you to win, it may simply mean that he wants you in the hands of someone with that distinct type of expertise. If you plan to appeal, make sure that your trial lawyer files a Notice of Appeal with the trial court within 30 days of the date of your sentencing. If the appeal is not filed within that 30 days, an appellate lawyer may be barred from filing an appeal on your behalf.