There are many people who think that the two skills to playing good classical piano – improvisation and sight-reading – are mutually exclusive. That is to say, people that can sight-read can’t improvise, and people that can improvise can’t sight-read. At least that’s how the common saying goes. It’s false, however; you can do both if you learn properly.
You do need both skills, in fact, and need to be able to use them at command. Popular music generally isn’t going to allow you the luxury of having sheet music, especially if you’re a keyboardist. You just don’t have room for a stand and music on the stage. This is where knowing how to improvise and play by ear comes in handy. On the other hand, if you’re asked to sight-read for a recital, for instance, you need to know how to read music. Classical piano lessons can help you learn both. 
As a classical pianist, your classical piano lessons can enable you to run through your library of music and learn new music, all to better yourself as a pianist. There are a few simple practice drills you can do during your classical piano lessons to hasten this process.
First, learn to understand chords. As you’re practicing a piece of your sheet music, take a look at the chords you’re playing and break the chords down into their component notes. For there if you want to improvise by changing major chords to minor or vice versa, you can. A good example of this is in the first few measures of Fur Elise, where there are A minor and E major chords. Once you learn these, you can shift them around as you see fit and can weave them differently into the song. Also, you can somewhat memorize the music by learning its underlying chords, because classical music lessons teach that many classical pieces have recognizable scale progressions built on chords.
In addition to chords, try learning a few lines of the main melody of whatever song you’re practicing. This gives you a mental library of phrases to improvise from. Personally, I like taking the melody of Sakura and tweaking the key signature to create the accompanying harmony part. Melodic phrases and classical chord progressions abound in classical piano pieces.
Likewise, take some time to play the various scales that you may find in your classical piano pieces. Not only do you get good practice in playing scales, you also can gain a sense for melodies and chords. Practice arpeggio runs as well, because these are often used. To increase finger dexterity, play scales at higher and higher speeds so that you know them quickly enough to play them without having to think what note comes next.
With classical piano lessons, you can learn to improvise songs and learn more aspects of music theory by analyzing the basic components of music: scales, chords, and the main melody. Once you understand the basics by breaking songs down, you can put them back together in new ways.
As you continue to progress through the lessons you may want to check out a few more styles such as blues piano and jazz piano. Also you can see how you can learn at home with online video piano lessons and how essential online piano lessons are to your success as a pianist.
Learn more about classical piano lessons by visiting the main page of PianoLessons.com, or by browsing through a few of our other piano lesson articles that we have posted on this web site.