The question of how to improvise music actually has a simple answer. Without sarcasm, the answer is a question in itself:
What’s stopping you?
A continual iteration of the question and resolution of the answer is the process of learning improvisation.
Among other things, improvisations are meditations navigating worry. We attempt to play, avoiding a servitude to the whims of anxiety. The success to which this practice is achieved is reflected in the landscapes of tension and relaxation that unfold throughout a piece.
Listening intently to music created in meditation allows a view towards understanding and moving through these very ancient and powerful emotions which, ultimately, stem from our concern for survival. Connecting these primal states to our conscious selves in ebbs and flows common to all nature moves us away from anxiety away and towards ease.
A piece of music created from tension feels disturbed. It leaves a listener with a sense of incompleteness, mistakes, errors, and ultimately a discomfort ranging from nuisance to pain.
As I sit at the keys, I wonder, Where is my anxiety? What is keeping me from being relaxed at this moment? Have I have done the work of placing my mind at an honest ease?
When I have well answered these questions, I may better enjoy a free play.