Practice. Experience. Lather, rinse, repeat.
If you do a certain chord change or progression often enough, and in different songs, you can hear it.
You can listen to a song and actually think "Hm. This change would fit in here."
I am by no means a GREAT Organist, but you don't have to be great or play for 10 years before you begin to hear changes.
Practice. Experience. Lather, rinse, repeat.