Short list of various listening exercises proposed by R. Murray Schafer, Agnes Szeląg, Jonáš Gruska and others. They are designed to help you with your aural focus, hearing sensitivity and might even stimulate your creativity.
Interesting way to temporarily sensitise your hearing: plug your ears with earplugs/cotton for at least 15 minutes. The better isolation you can make, the better. Remove the plugs just before the listening opportunity – you will notice your ears will be much more sensitive to the details for few minutes.