Just in case there are some people who still don't understand the circle of 5ths, here is another way to look at it:
The circle of 5ths tells you how many sharps or flats are in each key. Moving clockwise (right), the notes move in 5ths. Moving counter-clockwise (left), the notes move in 4ths. I can't show you a circle, but I can put it in a form that illustrates this, u can try to draw it if you want to:
C = 0 sharps or flats (12 o'clock)
G = 1 sharp; F# (1 o'clock)
D = 2 sharps; F#, C# (2 o'clock)
A = 3 sharps; F#, C#, G# (3 o'clock)
E = 4 sharps; F#, C#, G#, D# (4 o'clock)
B/Cb = 5 sharps; F#, C#, G#, D#, A# (5 o'clock) / 7 flats; Bb, Eb, Ab, Db, Gb, Cb, Fb
F#/Gb = 6 sharps; F#, C#, G#, D#, A#, E# / 6 flats; Bb, Eb, Ab, Db, Gb, Cb (6 o'clock)
Db/C# = 5 flats; Bb, Eb, Ab, Db, Gb (7 o'clock) / 7 sharps; F#, C#, G#, D#, A#, E#, B#
Ab = 4 flats; Bb, Eb, Ab, Db (8 o'clock)
Eb = 3 flats; Bb, Eb, Ab (9 o'clock)
Bb = 2 flats; Bb, Eb (10 o'clock)
F = 1 flat; Bb (11 o'clock)
The keys C# and Cb aren't usually present in the circle (i just added them there), but there is a reason why. Notice that the circle starts with C, having no sharps or flats. Now, the key of C# has everything being sharped, and the Cb has everything being flatted. So, what you can do is make a separate circle for the sharps, and a separate circle for the flats, and it could go on forever. I'll show you a little of each:
Sharps Circle
C = 0 sharps (12 o'clock)
G = 1 sharp; F# (1 o'clock)
D = 2 sharps; F#, C# (2 o'clock)
A = 3 sharps; F#, C#, G# (3 o'clock)
E = 4 sharps; F#, C#, G#, D# (4 o'clock)
B = 5 sharps; F#, C#, G#, D#, A# (5 o'clock)
F#= 6 sharps; F#, C#, G#, D#, A#, E#
C# = 7 sharps / all sharps; F#, C#, G#, D#, A#, E#, B# (12 o'clock)
G = 1 double sharp; F## (1 o'clock)
D = 2 double sharps; F##, C## (2 o'clock)
A = 3 double sharps; F##, C##, G## (3 o'clock)
etc.
Flats Circle
C = 0 flats (12 o'clock)
F = 1 flat; Bb (11 o'clock)
Bb = 2 flats; Bb, Eb (10 o'clock)
Eb = 3 flats; Bb, Eb, Ab (9 o'clock)
Ab = 4 flats; Bb, Eb, Ab, Db (8 o'clock)
Db = 5 flats; Bb, Eb, Ab, Db, Gb (7 o'clock)
Gb = 6 flats; Bb, Eb, Ab, Db, Gb, Cb (6 o'clock)
C = 7 flats / all flats; (12 o'clock)
F = 1 double flat; Bbb (11 o'clock)
Bb = 2 double flats; Bbb, Ebb (10 o'clock)
Eb = 3 double flats; Bbb, Ebb, Abb (9 o'clock)
You see that? Theory stuff can go on into infinity, but to make things easier, we try to keep it as simple as possible. Can you imagine trying to read music containing a bunch of double sharps and flats?
Like I said, this is just another way of explaining this concept. If anyone else wants to add in some stuff here, feel free to do so. I'm making this a sticky so the information will always be visible.