Let the music speak for itself.
Well David "Fathead" Newman was my first experience with improvisation. When I saw him play for the first time I realized that there is an importance of spontaneous music being made on the spot. It was so soulful and singing through his horn. So that's how I was inspired early on.
Well I mean I just sit at the piano and maybe figure out some harmony or melody or both. Sometimes you can hear it in your head. Sometimes you don't always have to write it down. You just write it down so you can remember it.