Yes, this is it. The Holy Grail. Beginning on any of the 12 notes you can construct major/minor scales and the chords that go with them. The relative minors are already attached to the major keys, so you don't have to work them out. If you wanted to, it's always 90 degrees clockwise. That is to say, for instance, and A is 3 steps clockwise from the C. Another way to find it is the relative minor begins on the 6th degree of the major scale. Counting up from C, A would be the 6th note.
As you count up by 5ths, for instance G being the 5th note of the C major scale, you land on the next spot on the chart. Each time you do another sharp is added. (Or another flat is removed if you go far enough.) This sharp (the last one) is always the 7th note of the major key.
Sharps are always added in the same order and they also ascend by 5ths. The first is F#, the second is C# and so on. This is if you go clockwise. Going in the counterclockwise direction you would be ascending by fourths, adding flats or removing sharps as you go.
So why is this important?
The different positions of the scale induce a different feel relative to the the first one which is commonly called the root, although it's more properly referred to as the tonic. The way two notes sound together is called consonance (their agreeability) or dissonance (the yuck factor). Two instruments playing the same note is the most consonant. Next would be two notes an octave apart. After that two notes a fifth apart followed by the fourth. This is because of the harmonic content of the notes. The nearer any two notes are to each other on the circle of fifths, the better they will sound together. The most dissonant are the two on opposite sides (180 degrees) from each other.
Another aspect of the circle of fifths is that any two adjacent keys have the most notes in common. Many popular songs, whether based upon a major or a minor key, commonly center around the root, fourth and fifth. The entire genre of blues depends upon it. As you can see these are always right next to each other.
You might be able to map it out on YOUR instrument as we begin to talk about tuning.
