You can improve your psychic hearing the same way you improve your physical hearing:

PAY MORE ATTENTION TO ALL SOUNDS.

Not just for a while, but ALL the time. Most people are NOT sound oriented. Thousands of sounds pass us by every day, without us hearing even a whisper. Where ever you go, pay more attention to all the sounds. Make friends with all the variations. Get to know them. See the subtle differences? Pay more attention-- to your own voice. Listen more closely to the voice of others. Not just what they say, but the tone of their voice-- the quality of the sound.

How does a idiot savant have perfect pitch and learn to play the piano perfectly by ear? Savant's are obsessive. At a very early age they become obsessed with the sound of notes and music. It's all the ever think about. It's sustains them. It becomes them. Do that for a few years or ten years, and your results will be equally remarkable.

Just can train yourself to become obsessive about all the sounds you hear. You probably won't be able to do this in short order, but ask yourself, is this what you want in five years?

When you start remembering sounds you hear in your dreams, you know you're on the right track.

Start learning an instrument. There is a a grand tradition of musical training that can be invaluable in your psychic endeavors.