In many criminal cases, there's nothing left do after you've been sentenced on a criminal conviction. The sentencing judge hands down your sentence - the punishment for committing a crime - and technically, the case is over. However, unless the case involves a traffic offense or other minor crime, a criminal sentence usually is a very serious matter. You may be looking at months or even years in jail. Because they're serious, it's not uncommon for defendants to appeal their sentences. This is a complicated process, and it requires filing paper work, meeting deadlines, and having a good reason and proof that your sentence is wrong.
An appeal may be filed by either the prosecution or the defendant (on appeal, the defendant is called the "appellant"). It's when one of you doesn't like the outcome of the case and asks another judge or a higher court to look at the case again for errors or mistakes. Usually, the court on appeal doesn't re-weigh the facts or the evidence. That is, it doesn't make a new, independent decision about whether you actually committed the crime. Rather, it looks at the case to see if the judge who made the decision - in your case the judge who sentenced you - made some sort of a legal mistake that makes the sentence wrong or unfair.
There are very strict rules you need to follow in an appeal. There are separate rules for federal courts, and each state has its own rules, which are usually very similar to the federal rules. To start an appeal, you need to file a certain form with the clerk of the court where you entered your plea. In the federal courts, and in many state courts, this form is called a notice of appeal.
One of the most important rules to keep in mind has to do with how long you have to file your notice of appeal. If you don't file it in time, it's very likely that a new court or judge won't look at your case. Generally, in federal courts, you have to file the notice within 10 days after the judge made the sentencing order. This time may be different if your case was in state court.
Also, you have to write and file an "appellate brief." This basically explains to the court why you think the sentencing judge made a mistake. The prosecution or government must also file a brief, which tries to explain why your sentence shouldn't be changed. You can file another brief (called a "reply" brief) if you want to disagree with anything in the prosecution's brief. There are time limits here, also. Generally, you have 40 days after the notice of appeal to file your first brief, and then 14 days after the government's brief is filed to file any reply brief.
An appeal is usually a complicated process, so you need to carefully read the rules for the court where the appeal will be heard to make sure you're doing things right. It is possible to handle the appeal by yourself, but it's usually not advisable. If you're thinking about filing an appeal, you should talk your attorney.