To understand the chord progression, you must first understand the musical scale. In the C Major scale, the notes are C, D, E, F, G, A, B and C. If a song is in the key of C, it will utilize the notes of the C Major scale.
From the notes of the C Major scale, you can extract the tonic (I), subdominant (IV) and dominant (V) chords. These chords are the most common chords used to form progressions in music.
The tonic chord (composed of the notes C, E and G) is derived from the bottom note and every other note up to G. The subdominant chord (composed of the notes F, A and C) is derived from the fourth note in the scale and every other note up to C. The dominant chord (composed of the notes G, B and D) is derived from the fifth note of the scale and every other note up to D (the scale must be repeated).
The chord progression can then be realized by creating any combination of the I, IV and V chords. This may include I to V, IV to V, I to IV to V and V to 1.
A good example of a chord progression can be found in the popular song "Like a Rolling Stone" by Bob Dylan. The chord progression of the entire song is I (tonic), IV (subdominant), V (dominant), V. If you were to play the song in the key of C, you could derive every chord in the progression from the information in this article.