Learn the chromatic scale by understanding that it is made up of all the notes in one octave. The octave is arranged in half steps so that any one note on the piano keyboard is one half step away from the note closest to it; therefore, a one octave chromatic scale will be made up of the 12 notes that are arranged between the bottom note and the top note. A chromatic scale can start on any pitch, but for this purpose, the chromatic scale will go from C to C. See keyboard illustration with notes of the chromatic scale.
Become proficient in the construction and reading of the major scale. All major scales are built the same regardless of the note on which they start. Major scales are made of two tetrachords with a whole step in between. A tetrachord is a series of four notes containing two whole steps followed by a half step. The C major scale would start on C, followed by D one whole step above. The D would be followed by E a whole step above, giving the first two notes of the tetrachord. F, one half step above E would come next, completing the first tetrachord. The second tetrachord would start on G a whole step above F. A, a whole step above G would come next, followed by B another whole step up. The second tetrachord and the C major scale would be complete by adding C a half step above B.
Memorize the structure of the harmonic minor scale. There is a whole step between the first and second steps (C to D in a C minor scale), with a half step between the second and third notes (D to E flat), followed by whole steps between the third and fourth steps (E flat to F) and fourth and fifth steps (F to G.) There is a half step between the fifth and sixth steps (G to A flat) and one and a half steps between the sixth and seventh steps (A flat to B). The harmonic minor scale is complete with a half step between the seventh step and the last step (B to C).
Know that the sharps and flats at the beginning of each line tell what notes are affected by them. A "C" scale will have no sharps or flats. The flat major scales go from F with one flat; B flat, 2 flats; E flat, 3 flats; A flat, 4 flats; D flat, 5 flats; G flat, 6 flats; and C flat, seven flats. The major sharp keys begin with G, one sharp; followed by D, 2 sharps; A, 3 sharps; E, 4 sharps; B, 5 sharps; F#, 6 sharps; and C#, seven sharps.