There are several potential reasons for airiness. It could be that you're expending more air than necessary as you play, which would mean you need to conserve your air supply more (which will also help with longer phrases). You might be experiencing some leaks in the flute, or simply have a headjoint prone to producing wind noise. Try recording yourself from a distance and see if the air noise comes through. You may need to focus your airstream more carefully into the edge of the embouchure hole. Any of these (and probably more I haven't thought of) could be the cause for airiness. As for improving tone, what exactly is wrong with it? If you're looking for a stronger, darker sound, be sure to open your airways as much as possible (sometimes termed "opening your throat and dropping your jaw"), and try to direct the air down into the flute more.