hearing the words "just improvise" doesn't help much does it---but it's true. If you have a heavy classical foundation---it gives you great chops--but it can also prevent you from realizing what jazz is. It kinda flies in the face of what you've been taught classically wise.
It is important to understand theory--both traditional and jazz. It is also important to basically know every chord, inversion, extension, there is and be able to play it immediately--which is not nearly as hard as it sounds. Jazz has it's standard chord progressions, too.
Ear training is essential.
Most of all--improv--for me, anyway--comes from the part of my brain that made up songs as a kid. The part that wasn't afraid to play what I heard in my head.
Really there is no sheet music that can teach you how to improvise. Scales, arpeggios, riffs--yes practice them--in different rhythms and keys.
the process... just start doing it. You will feel afraid at first. You may hate every note you play--ignore it and push on. Pay more attention to rhythmic accuracy than to tonal accuracy. Listen, listen, listen to jazz. Since you like Oscar--start with Night Train...great tune--and not very difficult.
You will eventually realize that it is not nearly as hard as you thought it was--then one day you will wake up and you will be able to play a little bit--- then things will start to make sense. It's a long process.
There are books like the Jazz Language by Dan Haerle, Effortless Mastery by Kenny Werner, or How to Practice Jazz--Leslie Coker--
I liked them and learned quite a bit from them. Actually, Dan Haerle was my teacher at UNT so I am a bit biased to that one. Good luck
