Many pianists have asked me, "how do I learn to improv?"
This question has simpler answer than many would expect, so let's dive into some helpful tips to get you started.
Let me preface with this: you do not need to be a seasoned pianist with years and years of playing experience. All of this is built on basic music theory. It's easy to see someone sit down at a piano and play something without sheet music and think, "wow, how are they doing that?!" but it can actually be much easier than complicated sheet music. We are talking about playing from a chord progression or a chord chart.
One summer during high school, I took a course that focused on chords. It was just the basics, like what's a "C" chord, or "F minor." From there, we talked about how chords worked in a key signature, and what chords were common. For example, in the key of C, your common chords would be C, F, G, and A minor. Still tracking? Let me explain why as we go one step deeper:
In a key signature, we can assign Roman numerals to scale degrees. So, I is scale degree one, IV is scale degree four and so on. Common chords are the chords built off of scale degrees one, four, five, and six, or I, IV, V, and vi (minor chords are lowercase). Use this common chord progression for practice:
C - G - Am - F
(I - V - vi - IV)
From here, we talked about inversions. So a chord in "root" position (root of the chord is the bottom note, i.e. a C chord, root is C) might be spelled C E G. An inversion of this chord could be E G C. All we do is reorder them. This helps us position the chords in places that fit the hand more easily.
In the left hand, add the root as a single note, or in octaves. Something I like to do is arpeggiate the left hand. So maybe for a C chord, you would play C - G - C while the right hand plays the chord.
With practice, playing chords like this will come more naturally, and paired with an understanding of the chords from a music theory perspective, this will translate easily to any key.
The last thing I want to mention is this: make this type of playing your own! I began to develop my own style over time as I played this way. Learning where to play notes in between chords, or where to drop notes from the chord altogether are just a couple of ways to begin creating your own unique style. Maybe take out the third, and just play the root and the fifth. Try moving the third of the chord to the second instead. (C, D, G).
I hope these tips will encourage you to get back into playing, try something new with your playing, or take you to the next level as a musician!