Every music student needs to make audition recordings these days, and so I've put together some tips for making yours the best it can be. While these tips are specifically for audio recordings (without video), most of these tips can apply to video as well.
1. Start early.
Make sure you know all the requirements and deadlines several months ahead of time. Rushing around a couple of days before a deadline is definitely not the way to go! Book your recording space--and everyone else involved--early. And make sure your accompanist has the music early too. Talk to your teacher as well--he or she is your single best resource in helping you prepare!
2. Practice, practice, practice!
The single best way to improve your audition recordings is to improve your performance. Even with the best recording equipment, a lackluster performance will translate into a lackluster recording. Problems with intonation, dynamics, tone, and musicality cannot be properly fixed after the fact. And if you're making mistakes in practice, you'll almost certainly make the same mistakes in performance. Your teacher should be able to help you with these things (if not, it's time for a new teacher!). Also, make sure to spend adequate time rehearsing with your accompanist. While a good accompanist can give a good performance with minimal rehearsal, a little extra rehearsal time will make everyone feel more comfortable.
3. Make sure your instrument is in proper working order.
If your instrument isn't working properly, you won't be able to give a good performance. For wind players, things like loose screws, leaky pads, or a finicky reed can cause trouble. String players need to make sure that their instruments are properly set up, and that their bow hair is in good condition with the right amount of rosin. If you are a pianist, the available instrument should be part of your choice of recording space (see #5). Whatever you play, a professional tune-up of your instrument will make sure that it's in top playing condition. If your instrument still does not perform adequately, it may be time for a new instrument.
4. Perform your repertoire before recording it.
Before you record anything, perform it in public, preferably several times. While you may be able to play a piece perfectly in practice, performance is entirely different, and the experience of playing a piece "on the spot" is very valuable. Live performance will also reveal any places where things don't quite work musically, or easy passages that suddenly become difficult when nerves kick in. Recording your performances will also give you a chance to hear exactly what happened and make any necessary adjustments. Even a smartphone recording will do, though a dedicated handheld recorder will yield better results, and might even result in a recording that you can use for an audition!
5. Find a good space to record.
Make sure that the place that you choose to record is quiet (free of traffic, HVAC, and other noises), and has a good acoustic. I have made some good recordings in my piano teaching studio, but it's less than ideal. Also make sure that no one will be making extraneous noises (like opening or closing doors) as you play. If you have an accompanist, make sure that you have a properly working, well-tuned piano (preferably a grand, even better if it's at least a 6-foot model) available for your use. Professional musicians will often keep a piano tuner/technician on standby for recording sessions, but you have to decide if it's worth the expense.
I haven't mentioned anything yet about recording equipment. This is because the quality of the performance, the acoustics of the room, and microphone placement are vastly more important than having a room full of high-end equipment. Stay tuned for Part 2, which includes some tips for equipment, and some tips for the day of the session.