The ultimate goal in improvisation is to be able to bridge the gap between your mind and your instrument. This is achieved with the regular practice of ear training. Jazz utilizes complex harmonies, and in order to improvise over these chords, the improviser needs to have an adequate aural awareness. When operating solely on knowledge or theory, the improviser will sound like she is "running scales," and will be unable to respond to alterations of the chord that may occur spontaneously within the rhythm section.
Transcription is one of the most common forms of ear training for jazz musicians. Transcription is learning, by ear, solos of your favorite artists and songs they perform. This task can be tedious at first, so it is important to start with solos that are within your ears' current capabilities. Once this is done with some ease, it can be helpful to transcribe the chords to tunes you enjoy. This will help you hear what the rhythm section is doing as well as begin to recognize common song forms.
Many musicians whose primary instrument is not piano find it beneficial to gain some proficiency on the instrument. Learning standard tunes on the piano reinforces key concepts such as harmonic movement and chord voicings. Additionally, if you play a transposing instrument, this is a way to immediately learn tunes in different keys. Many people find the ability to visualize what they are hearing helps them make connections to the sounds.
Modern technology has created numerous ear-training aids. Play-along CDs are quite popular. These allow you to practice standards with a recording of a rhythm section so that you hear the changes and form. The website Musictheory.net offers ear-training aids that include scale, interval and chord identification. The Songtrellis website offers MIDI files of the changes to countless jazz standards. There is also a tool on the page that transposes the changes into different keys. Practicing in uncomfortable keys will force you to rely on your ears to make the changes.
Practicing ear-training exercises will develop your aural awareness. This can be done by yourself or with others. Interval training can be done with a piano, even if you have no proficiency on the instrument. Making sure not to look at the keys, play two random notes in succession. Identify the interval between them, and then double-check by looking at your fingers. Once this is done with ease, you can do the same exercise with chords. When practicing with another player, a fun exercise can be to play call-and-response games. One player plays an idea, and the next player plays it back. The difficulty in this exercise is only limited by your imagination.