When a note must be raised in pitch by a semitone ( one fret ) the sharp sign is placed directly in front of the note on the staff. In the example below, the second note in each bar has a # ( Sharp ) sign placed in front of it. The note has been changed from a C note to a C# note, and is played one fret higher on the fretboard. The important thing to note ( excuse the pun :) is that the bar line has cancelled the effect of the sharp. That is why the first note in the second bar is a C 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 made sharp. Notice that the effect of the sharp has also changed the second note to a C# as well.The sharp 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 sharp, consider the B7#9 chord.. Which is made from the 1st, 3rd , 5th ,b7th and #9th notes from the B major scale. Using this chord formula the notes from the B Major scale would be; B (1), D# (3rd), F# (5th), A (b7th), and C Double Sharp (#9th) . The ninth (or second) is already a sharp, so in order to raise it another semitone it must be Double Sharped.