I understand what the circle of fifths is and its layout, but all I've understood how to use it for so far has been using it to remember the fifth of a certain key (e.g. G is the fifth of C major). What else is it used for?
It helped me to memorize the key signatures, as well as to understand the relationships of the keys to each other. This in turn made it easier for me to analyze music.
To summarize the video above, the circle of 5ths is just a way that we have organized the different keys in music in a way that makes sense! It helps to visualize how keys/key signatures are related to each other
A great way to use the circle of fifths is to help remember the notes and key signatures that are in each major and minor key. As you move by a fifth in either direction, you will add a new sharp or flat to the key signature. These new accidentals ALSO move by fifths from the ones in the previous key, which makes it much easier to remember which keys have which notes. For example, if you can remember that G major includes an F#, then when moving the key up one fifth to D Major, you would know to include F# as well as C# (one 5th from F#).
The circle of fifths is often used to determine how many sharps or flats a given key has. C has zero sharps or flats and so it is placed at 12 o'clock. If you go clockwise, you add one sharp and counter clockwise adds a flat.
It also can be very helpful in terms of figuring out how best to modulate to a new key center. Each key is placed next to a key that has all but one note in common. This makes it easier to smoothly transition.