The Circle of fifths is divided in two parts, the key signature with sharps and the ones with flats. These two circles are used as cheat sheets to figure out all the key signatures.
The Circle of fifths in sharp works clockwise. Start from the key of C, because it's the only key signature with no alterations (# or b). Then you go a perfect fifth higher, which takes you to the key of G. Find the major 7th of G and you'll find the first alteration, so in this case F#. Then, you keep going clockwise. The perfect fifth of G is D and the major 7th of D is C#. So, the alterations in the key of D are F# and C#. Keep adding on to the alterations you find at the beginning of the circle until you have seven sharps.
Once you know what are the sharps in the key signature that you were interested in, you simply write your scale one note at a time, but adding the sharps. Per example, if you are looking for the key of E. You know that E has four sharps, therefor the scale is : E, F#, G#, A, B, C#, D#, E.
Circle of Fifths (#)
If you notice, at the top right of the circle of fifths in sharp, you can find the order of sharps: F#, C#, G#, D#, A#, E#, B#. If you have your key signature written on a staff and you are wondering which key it is. Check the last sharp and add half a tone to it, it will tell you what key you are in. Per example, if you know that your last sharp is A#, then you know you are in the key of B
The circle of fifths in flat works counter-clockwise. So, you start from the key of C, then you find the perfect fifth before. So, from C, the perfect fifth before is F. To figure out what flat will be part of the key signature of F, you simply find our what the next perfect fifth before is. So, the alteration in the key of F is Bb.
Circle of Fifths Flats (b)
The order of flats is : Bb, Eb, Ab, Db, Gb, Cb, Fb. If you look closely, you might notice that it is the complete opposite of the order of sharps, which means that if you memorize one of the two orders, you can simply reverse it to get the other one.
Here is how to write the order of sharps and flats on a staff with a treble clef and bass clef.
Key Signatures on staff
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