When a note must be lowered in pitch by a semitone ( one fret ) the flat sign is placed directly in front of the note on the staff. In the example below, the second note in each bar has a b ( Flat ) sign placed in front of it. The note has been changed from a B note to a Bb note, and is played one fret lower on the fretboard. Note that the bar line has cancelled the effect of the flat. That is why the first note in the second bar is a B natural ( a natural just means the note has reverted back to its natural state, not sharp or flat).

In the example below, the first note in the bar has been flatted. Notice that the effect of the flat has also changed the second note to a Bb as well.The flat rules until it is cancelled by the bar line.

In this example the second note has a Natural sign in front of it, a Natural also cancels the effect of the accidental (sharp or flat).

This example shows how the same note in octaves above or below the note that is flatted are not affected.

This example illustrates the confusion that can arise by the use of Double Flats. I have chosen to use the rule that a Natural completely cancels out a Double Flat just as a bar line would. Notice that I have restated the flat after the natural to make the last note a Bb. According to some theory books a double natural is needed to completely cancel a Double Flat.

This last example shows how flats in a Key Signature affect all notes regardless of whether they are in the same octave or not.

In case your still pondering why or where you would need to make a note a Double flat, consider the A7b9 chord.. Which is made from the 1st, 3rd , 5th ,b7th and b9th notes from the Ab major scale. Using this chord formula the notes from the Ab Major scale would be; Ab (1), C (3rd), Eb (5th), Gb (b7th), and B Double Flat (b9th) . The ninth (or second) is already a flat, so in order to lower it another semitone it must be Double Flatted.