Judgment And Post-Judgment:
At the end of the trial the judge will normally announce his or her decision. Sometimes, however, the judge will want to take additional time to review the evidence or research case law before entering a final judgment. This is called taking the case "under advisement". When this occurs, you will receive a copy of the final judgment in the mail after the judge makes his or her decision.
Different jurisdictions have different rules regarding motions for appeals and request for a new trail. In either case the motion must be in writing. In some jurisdictions like California, there are no appeals. The judgment is final. In other jurisdictions like New York only a defendant can file an appeal or the plaintiff if "substantial injustice" was done. In states like Ohio either party can appeal matters of law, not fact within 30 days of judgment. In some states such as Michigan either party may file a motion for a new trial within a specific number of days from entry of the judgment. Check Picking the Right State for more information. Depending upon the rules in your state the appealing party will be required to post a bond and either party may be able to request a jury trial.
To appeal a decision, if available, you must file a notice of appeal with the clerk of the Superior Court, Circuit Court or similar court in your jurisdiction. In most states an appeal must be filed no later than 10 to 30 days from the date judgment is entered. Again check your jurisdiction, as for example in D.C. you have the option to request that the judgment be "stayed" (not take effect immediately) because you intend to appeal. A motion for judicial review must be filed with the clerk within 10 business days.
An appeal is NOT a new trial. You are not allowed to present new facts or retry old facts. You are only permitted to argue errors of law, not fact based upon the record of the hearing. Therefore you may want to consider requesting that a court reporter be present to preserve the record. As you will be in Superior Court and formal rules of civil procedure and evidence will apply, you may want to consult an attorney if you choose this course of action due to the complexity of the rules and procedures.
To request a new trial you must file a written motion with the clerk of the Superior Court, Circuit Court or similar court requesting a new trail. Be sure to check with the court as the time limit to file from the day judgment is entered varies from jurisdiction-to-jurisdiction from on average 5 to 10 days. In some states, such as D.C. you will have the option to request a new trial by filing a motion for judicial review that must be filed with the clerk within 10 business days. If the review is denied you will only have 3 business days to file your appeal to be heard in D.C. Court.
You have to enforce your own judgment. The court in most states will not run after the defendant for you. The court's judgment, in itself, is nothing more than an official statement in the court's records that the defendant owes you a specific amount of money with interest. The judgment must be enforced out of the assets of the defendant. An airline as a large corporation in a small claims case is typically not going to appeal a judgment. They will normally pay the judgment and move on because to fight paying the small amount once a judgment is entered would far exceed the damages owed, including accruing interest.
However, if the airline refuses to recognize the judgment there are several things you can do to enforce collection of the judgment. You may also contact the court clerk as well as legal aid organizations for more assistance.