Once upon a time, all classical pianists improvised. Some improvised well, and some badly, but they all spent at least some of their time at the keyboard creating spontaneous music.* Although improv has been largely absent from the classical music scene since the late 1800s, many classical pianists now want to re-claim this grand tradition, and experience the joy of musical improv for themselves. This is an exciting musical time to live in!
If you've exclusively been playing written music for years, it can be a little scary to improvise. It's like an artist looking at a huge blank canvas, saying "What do I do now?" Infinite possibility often results in artistic paralysis. But if someone were to ask you to draw a house, with 4 windows, a door, and a chimney, using only brown and blue markers, then you could do it. As the composer Igor Stravinsky remarked, the more limitations we place on our art, the more freedom we ultimately have.
It's great that you want to improvise; you just need a way to get started. To successfully learn to improvise, there are really two separate aspects to pursue, sometimes at the same time. The first, which is most often overlooked, is to simply start improvising, using the vocabulary you already know. Major scales, triads, simple accompaniment patterns, etc. I've found that many of my classically-oriented music students are so used to the sophisticated sounds they make while playing written pieces that at first they need to relax their critical thinking mode, at least for a while. Just become like a young child learning to speak. Have fun and play simple melodies that flow up and down the scale. Once this mindset is embraced, the magic will start happening. Beginning improvisers have reported powerful feelings of joy and freedom, sometimes from their very first attempts, provided they can relax enough to let go of their usual musical expectations. And remember, what sounds simple to a trained pianist often sounds beautiful to a listener, so become a listener yourself as you are improvising.
If you also want to play another genre, such as jazz, rock or the blues, then the second aspect is to learn the specific vocabulary of whatever style you're ultimately interested in. Many classical pianists jump right to jazz and it's such a different world than they're used to that while yes, they learn the idiomatic chord voicings and riffs, they don't ever become fluent. It never becomes natural.
I've seen that the best approach is a well-rounded one, in which the player becomes fluent at improv by using the basics, and either at the same time or a little later, starts learning the specifics of jazz or whatever style they want. Best of luck; you'll experience music in a whole new, exciting way!
Here's a play-along video I made to get you started. Just place your computer and piano/keyboard near each other and follow my instructions. Have fun, and let me know how it goes or if you have any questions!
* Recent scholarship is gradually discovering how widely spread improvisation was in the classical music scene of the 18th and 19th centuries. If you want to learn more about this, I highly recommendI highly recommend Kenneth Hamilton's eye-opening book, After The Golden Age.
Get a weekly dose of musical inspiration and practice tips in your inbox. Simply enter your email address below (your email address will remain private) You’ll also receive a free copy of my ebook: Pop Ballad Accompaniment