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 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.