The circle of fifths is a very useful tool in music. It has many uses, more than I can say here. A fifth refers to the fifth note in a major scale, so starting at C on the top, if we see what the fifth note in the C major scale is (C D E F G A B), we get G, so G goes in the next slot. The fifth note of the G major scale (G A B C D E F♯), we get D as the fifth note, this pattern continues around, until we get to F, which has it's fifth note as C (where we started)

The first thing to notice is that the relative minor is on the next inner ring (A minor is the relative minor to C major etc)

The next ring inside the circle shows how many sharps or flats each key has, going clockwise from the top, the number of sharps increase, going anti-clockwise the number of flats increase (more about this later)

The order of sharps and flats

The order of sharps (♯): F C G D A E B

The order of flats (♭): B E A D G C F

Notice that the order of flats is the order of sharps in reverse. Let's look at the key of E major, we can see it has 4 sharps, but what are they. First of all write out the letters:

E F G A B C D 

Next count off the first four sharps from the order of sharps (F, C, G and D) and and a sharp symbol to each of the letters from above

E F♯ G♯ A B C♯ D♯ 

These are the notes of the E major scale, now let's try the key of B♭, so start by writing out:

B C D E F G A

count off the first 2 flats (B and E)

B♭ C D E♭ F G A

You may wonder why we've used flats on the left hand side of the circle and sharps on the right, let's look at the key of A♭, why not call it G♯?, I'll first use A♭ as an example

A B C D E F G

Add the four flats (B E A D)

A♭ B♭ C D♭ E♭ F G

Now let's try G♯

G A B C D E F

First of all we need 8 sharps! There are only 7 notes in the order, so we use F twice (add a double sharp symbol 𝄪), F double sharp is actually G

G♯ A♯ B♯ C♯ D♯ E♯ F𝄪

Apart from the confusing mess that is F𝄪 instead of G, we also have B♯ (C) and E♯ (F), this would make reading the stems very confusing