In my experience the single biggest reason guitarists have a hard time with the circle of fifths is because it is hard to visualize on their instrument. Literally, it is hard to SEE.

This is because the guitar makes no physical, visual distinction between a natural letter note and a sharp or flat. It's just another fret - one up or down.

Compare this to the piano and immediately the difference becomes obvious. If you are playing in G major on a piano the only black key you see and, or play is the F-sharp. Because the piano has it's very distinctive pattern of white keys for naturals and black keys for sharps/flats it is easier to see and recognize accidentals and key signatures.

Another problem is that many guitarist simply refuse to learn how to read music. The more a player reads on a regular basis, the easier it becomes to understand, see, and use key signatures, and thus the Circle of fifths. This is because the Circle of Fifths is frequently mentioned when the subject of key signatures comes up. It is a very handy way of unifying and visualizing all possible key signatures at once.

Each note is successively an interval of a fifth from the previous note. As you move from one note to the next, you add either a sharp or a flat to the key signature depending upon which direction around the circle you move.

We start at the key of C major (or A minor, which is C major's relative minor). The C major scale, and therefore the key of C major, has all natural notes (c, d, e, f, g, a, b) and therefore zero sharps or flats.

If we move up a fifth from C we arrive at G. Therefore one letter the right of C is G.

G is up a fifth from C. Applying the major scale formula starting at the note G results in the notes of the G major scale, and therefore the key of G major (g, a, b, c, d, e, f-sharp) and therefore it has one sharp.

We move up a fifth again from G to D. D is up a fifth from G. D is the next note to the right on the Circle of Fifths. Applying the major scale formula starting at the note D results in the notes of the D major scale, and therefore the key of D major (d, e, f-sharp, g, a, b, c-sharp) and therefore it has two sharps.

See the pattern emerging?

As we move clockwise around the circle, we are moving a fifth each time & as a consequence adding a sharp to each key signature in turn.

C major (A minor) zero accidentals (sharps or flats)
G major (E minor) 1 sharp - F#
D major (B minor) 2 sharps - F#, C#
A major (F# minor) 3 sharps - F#, C#, G#
E major (C# minor) 4 sharps - F#, C#, G#, D#
B major (G# minor) 5 sharps - F#, C#, G#, D#, A#
F# major (D# minor) 6 sharps - F#, C#, G#, D#, A#, E#

Notice also that the sharps are added in fifths as well!