Have a look at this scale of G:

In the scale of G, and therefore in the key of G, all the F’s are sharpened. The key signature for G looks like this:

The key signature tells you that in the key of G, all the F’s are sharpened. Once you add a key signature to a piece of music there is no need to add a sharp to all the F’s in the piece of music. When a scale of G is written with a G key signature, the scale would be written like this: