Understanding how to read these chords is simple - the letter to the left of the slash is the type of chord - so in this case it is "C" chord (aka a C major chord). The note to the right of the slash is the bass note in the chord - a "G" in this circumstance. So, a C/G chord is a C major chord with the note G in the bass. If you study the chord in part three, you can clearly see the C major chord, with the G on the third fret of the sixth string also being fretted in the bass.
Here are a few of the many common slash chords:
D/F# - (pronounced "D over F#") - a standard Dmajor chord with an F# in the bass, usually played by wrapping the thumb around the neck of the guitar, and fretting the second fret of the sixth string.
A/C# - (pronounced "A over C#") - An Amajor chord with a C# in the bass, usually played by barring the second fret of the fourth, third, and second strings with your first finger, and playing the fourth fret of the fifth string (the C#) with either the third finger, or the pinky finger.
C/E - (pronounced "C over E") - A Cmajor chord with an E in the bass, usually played by simply fretting a Cmajor chord, and including the open low E string in the strum.
Amin/G - (pronounced "A minor over G") - An Aminor chord, with a G in the bass, usually played by fretting an Aminor chord, and using the pinky finger play the third fret of the sixth string (the "G").