The best way to learn (nonjazz) improvisation is to do it – play and play, preferably with experienced partners who can model and advise and guide. Next to that (or along with that), it’s nice to not have to invent all the wheels yourself and have some books on the subject help you along.
The best ones to get (ahem) of course are mine (all published by GIA) Improvisation Games for Classical Musicians, Improv Games for One Player, Improv Duets, Improvised Chamber Music. But there are plenty of other books out there that you should consider looking at if you are interested in this subject. Here are some of them, not in any particular order:
Stephen Nachmanovitch, Free Play
William L. Cahn, Creative Music Making