The circle of fifths puts every key in a ring, each one a 5th above the last. Any key's 4 and 5 chords are its neighbours, so a key's three main chords are always three keys in a row: C–G–D for G major, F–C–G for C major.
Neighbouring keys share six of their seven notes, which is why songs move between them so easily. Inside the ring sit the relative minors: Em with G, Am with C, Dm with F. Pick a key below and its whole family lights up.
E major
Key signature 4 sharps: F♯ C♯ G♯ D♯
How to read it
Clockwise each key is a fifth higher and adds one sharp (or drops a flat). Anticlockwise is a fourth higher and adds a flat.
Rings. Each major shares its notes with the minor inside it (its relative minor) and the diminished chord on its 7th.
The chords of a key are the lit slice: three majors side by side (IV I V), the three minors under them (ii vi iii) and one diminished (vii°).
Neighbours differ by one note, so modulating one step round sounds smooth. Moving anticlockwise is resolving: V to I, and ii V I walks two steps home.
Secondary dominants. The major one step clockwise of any chord is its dominant (V of V: D to G in C major).
Try this
Pick a key next to G on the circle (C or D). Find its 1, 4 and 5 chords on the circle, then play them as 1 → 4 → 5 → 1.
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