Begin with both thumbs on middle C. Progress outward crossing the thumb under to hit the F (or fourth) note in the scale on the upper hand and the G on the lower octave on the hand progressing downward. If you are doing 2 octaves, continue to bring the thumb in to pick up the next note, until you're close enough to complete the scale with your entire hand.
Come back to middle C. As you bring your fingers back toward middle C, play 1 note on each finger and cross the third finger over to pick up the next note on the scale inward. Once you know the scales, you can begin advanced piano playing.
Play a series of C major chords. First use the middle C as the start of the chord, and use the fingering of 1, 3, 5. The notes to play in this chord are C, E, G. Next, invert the chord and start with the E as the first note. Use the fingering 1, 2, 5. The notes to play are E, G, upper register C. Finally, use the fingering 1, 3, 5 and begin the chord with G. Go to upper register C as the middle note and add upper E for the fifth finger.
Repeat the same exercise that you did in Step 3 but move the third finger down a half step, creating a minor chord. By doing this, you play C, E flat and G. Move up the chord to place the E flat in first position, just as you did with the major key. Do this exercise in other keys.
Find equivalent minor keys to major keys by taking the finger positions on the piano 3 half steps down. If you begin in a C major key and count backward 3 half steps, you hit B, B flat, A. A minor has no sharps or flats in its scale, just like C, and so it's the minor key that parallels C major.
Check out the key signature. Look for the sharps in the key signature and remember that the sharps go in a specific order, FCGDAEB. Go up a whole step from the last sharp on the piano and you can find the key in which it is written. Use the regular note to do this. If there's one sharp, then put your finger on the F, not the F sharp and go a whole step up to G. The piece is written in the key of G.
Reverse the order of sharps to find the key signature in flats. BEADGCF is the reverse of the order of sharps. To find the key signature in flats, find the next to the last flat and it's the key. If there are 3 flats, E flat, the next to the last, would be the key. If you can find the key, you're now ready to use the scales and chords to begin advanced piano playing.
Combine the information. Use the chording and runs for the key to fill in around the melody of the song. Even though you're simply doing finger exercises that you've learned, adding the chording and runs makes the composition sound full and professional.