Divide the song into its essential segments. Songs traditionally consist of several verses and a chorus. The verse and the chorus usually have different chord changes. In addition to the verse/chorus structure a song may have a introduction and a bridge.
Write down the chord changes for each segment of the song. If you are composing the song this step is easy. If you are learning the song by ear from a recording, this step is a little more difficult. The first step in learning a song by ear is to identify what key the song is in. A couple of tricks to identify the key are (1) Listen to the end of the song. Most songs end on the tonal center. (2) Focus on the bass guitar. The bass guitarist usually emphasizes the root notes for the chords and this helps to identify the chord changes.
Learn the fundamentals of music theory. This takes away a lot of the guess work when trying to learn songs by ear. Chords are not chosen arbitrarily, they follow a musical logic. The I, IV and V chords are the most commonly used chords in popular music - rock, country, blues, and folk music. In the key of C major, the I chord is C, the IV chord is F and the V chord is G.
Write horizontal lines for each measure on a piece of paper. A measure represents a unit of time in music. If the song is in 4/4 time, the measure represents four beats. If the song is in 3/4 time, the measure represents three beats. Write a segment of measures for the introduction. Write a segment of measures for the verse section and a segment of measures for the chorus section.
Write the chord changes for the introduction, verse and chorus. For example, a twelve bar blues in the key of C looks like so C / C / C / C / F / F/ C / C / G / F / C/ C. A eight bar country song in the key of F may look like F / F/ B-flat / F / F / C/ C. If a measure contains more than one chord, write both chords between the horizontal lines such as G C / G / G D / G.