You're not expected to shoot a professional-quality video, but do make sure it's good enough that you can be seen and heard clearly throughout before you send it.
Natural light is sufficient. But be sure to face your light source so you are not lost in the contrast.
Test your microphone and ensure there isn't too much background noise, so you remain audible throughout the audition.
Frame your shot so that your face is clearly and frontally visible in a medium close-up (the top of the frame should be slightly above your head and the bottom of the frame just below your shoulders). In other words: Your face should be your most visible part.
Keep your camera as still as possible unless there's a good reason to move it about. Use a tripod.
Unless you choose to film yourself on location, use a plain background if you can.
Avoid filming other people. Unless you're doing a monologue, have someone read with you, but don't film the other person. "They should be standing right next to the camera, and read your lines directly to them," advises casting director Marci Liroff. "Many times I see the actor is reading with their eye line so far off, it doesn't connect with the viewer."
Avoid fancy montages. This is more likely to make the casting director think you can't do an entire scene in one take.
If you're filming with an iPhone, be sure to hold it in landscape mode (horizontally, with the lens toward the top). Otherwise your video will either be very narrow or sideways when it's viewed (even though you won't notice this on your iPhone, since it automatically rotates the video).
If you're using a webcam, use your camera's software to increase the video frame rate to the maximum; otherwise your video will likely be choppy.
This list, based on the feedback of numerous casting directors, is provided courtesy of the website Let It Cast.