My top tip for improvising? Do it.
There is no requirement for it to sound good; there is no punishment for it sounding bad. When you're in the privacy of your practice room there is no one there to judge you but yourself.
Start by improvising unaccompanied. Pick a scale, and make a goal of playing every note in the scale at least once, but in an order you choose. Make sure to incorporate the other elements of music - like phrasing, rest, & rhythm! (We call this "Anyway Up" in Flutarians IMPROV GAMES!) The finesse will come later. Want to know the most effective way to accelerate your improvement? 👇