You need to know the key signatures of scales.
You need to know what scale is associated with what chord. To do that you need to be able to play chords, but I'd say you need that anyway. Play lots of chords, and concentrate on recognizing chord progressions. Just as you can hear a melody by just reading the notes on a staff, you can learn to hear chords in your head by reading them.
learn to hear the chords by just reading them. If you want to be able to play by the written chords, you can: train by singing short melodies first, then trying to play them on the piano. Watch also closely on which chords these licks work. listen a lot to known recordings of the song, and try to pick up phrases and licks that you like. You must really have the chord progression everywhere in your brain. Either with a play along recording, playing yourself, listening to known recordings. 
listen to the chord progression many times. The melody of a song is a good starting point for improvising, you can start by playing variations. CHORD PICKOUT KEY 3.0 HOW TO
Then you need to know how to play the notes that you are hearing in your head. You need to know the song's harmony by heart. If you want to go by ear, you need to know how the chords sound. Good improvisers are able to go either ways.
Soon you notice that it's not either one way or the other, it's a combination of both. Learn what tones fits the chords in the chart.
going by ear, just play something that fits. How do you know when it's okay to go outside the scale? But every now and again, by chance, it sounds so right. But whenever I try to do it while improvising, it usually just sounds dead WRONG, instantly. But I know from all the other pieces I've played that you don't have to stay inside the scale in order for it to sound right- obviously pieces have sharps and flats and naturals outside the scale all the time. For instance, if she said F major, she would show me that B is flat (because I don't know my scales by name), and then while improvising I would be careful not to hit any other black keys and not to hit B natural, which are not in the scale. Lastly: The way we improvise is my friend picks a key and shows me what the key is, then I'm careful to only hit notes in that key. How can I learn which ones achieve what kind of sound and when they'll belong and when they won't? But whenever I try to hit one, it just doesn't sound right. Obviously in all the pieces I've played written by other people, there are a million different chords of 2, 3, 4, 5, even 6 notes, and they sound beautiful. Problem two: while toying around with the melody, I'm pretty much trapped in single notes and octaves. How do you learn to know what notes to hit? Right now I just have to guess, and sometimes I get it, and sometimes I don't. I have no trouble keeping time with them, and I sometimes come up with very pretty melodies, but then here's what happens: I hit 2-3 notes and in my head I hear a melody continuing with the pattern of those 2-3 notes, but then I don't know what notes I'm hearing in my head (I don't have any sort of pitch, not even relative, I'm pretty much tone-deaf), so I can't continue the melody in real time because I don't know what keys to hit in order to create the notes I'm hearing in my head. They usually take the lower register and establish a beautiful rhythm, while I take the upper register and toy around with a melody. I play piano fairly well, but I skipped theory entirely in my early days and learned to play by reading sheets and listening to better pianists online playing the same piece I was learning, then carefully emulating their sound.īut now I've made some friends who like to improvise together on the piano and do it extremely well, and I'm at a loss when I join in. 
How can you learn to know when accidentals (notes outside the scale) will sound good?. How can you learn which chords will sound good where? There are so many types of chords, how can you know when to play a certain one?. How can you learn which keys to hit to make the notes you hear in your head? I know what I want to play when I'm improvising, I can hear it in my head, but I don't know which keys correspond to those notes. This is 3 questions in one, so it might take a slightly involved answer, or some good links.
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