Don't wear costumes or crazy get-ups. This might seem like the best way to get noticed, but it won't be the right kind of attention. The judges are likely to be paying more attention to your costume than your voice, and that is not going to win you a golden ticket.
Pick a song that fits your voice. You may love Celine Dion and Mariah Carey, but singing one of their songs is going to cause the judges to compare you to the original, and it's unlikely your version will stand up. Picking a song that you sing well will catch the judges' attention.
Pick an uncommon song or one the judges don't usually hear a lot in auditions. Most singers will be auditioning to the newest hit songs on the radio, so don't pick a song they are likely to have heard 100 times that day. You don't want to bore the judges and blend in with the rest of the people who auditioned with the same song.
Make the song your own. Add your own personal spin to make it sound new to the judges. Don't try to sound exactly like the original.
Ease your nerves. Take a few deep, calming breaths before your audition. Being at ease in front of the judges is a great way to impress them. Nerves are understandable, but they will not help you or get you noticed.
Be yourself and be genuine. A lot of people go into the audition and try to act crazy or obnoxious to get the judges' attention, so those who audition as themselves instead of a character are the ones who get noticed and treated as actual singers. Allow your voice to speak for itself, and you will get more attention than a crowd of costumes.