How do you prevent the airy sound on an alto saxophone?

Practice. More experience, the better sound. Also, the mouthpiece makes a big difference to the sound. The mouthpiece that comes with the Saxophone tends to (not always) be a beginner one, that is easy to use but is unable to hit the low and high notes. Whereas if you got a more professional mouthpiece, after you get used to it, it sounds much nicer and is easier to play. Another thing, by learning techniques like vibrato or 'growling', makes great effects when performing and recording. To do vibrato, move your jaw (fast) up and down ever so slightly when playing a long note; this makes it sound sort of echoey and like the sound is vibrating, hence the name 'vibrato'. To growl, make a humming noise whilst playing a note, and it makes an intense gnarly sound. Though it is quite tricky to do, so don't be put off if you can't do it after a few tries ;)

Remember though, saxophones that are on CDs are edited in sound. They put on echo effects and pitch corrector so it sounds perfect, which is extremely difficult to do playing live. So use recorded saxophones as a reference, but don't get upset if you don't sound exactly like it ;)