The first step in playing these three voicings will be to find the root note of the major chord you want to play on the sixth string. Then, play the first chord voicing above, making sure the root of the chord (marked above in red) is on the root note of the major chord you're trying to play. You'll probably want to finger the chord as follows: pinky finger on 6th string, ring finger on 5th string, and index finger on 4th string. VOILA! You're playing an major chord shape that you didn't know before. This is often referred to as a "root position" major chord, because the root note is the lowest note sounding in the chord.
There are two ways to figure out how to play the next chord illustrated above. The first would be to find the root note on the 4th string, and to form the chord shape around that. Many of you will find this difficult, since it's not common at first for guitarists to learn the note names higher up on the 4th string. Alternately, try the following: from the note you just played on the 6th string, count up four frets. This will be the starting note for the next chord shape. Plunk your fingers down (I might suggest ring finger playing the note on the 6th string, and the index finger barring the 5th and 4th strings), and you have another way to play a major chord. This type of chord is often referred to as a "first inversion" major chord, since the root note is no longer on the bottom. Try moving back and forth between the root position and first inversion chord. Eventually, you will get a feel for how far the distance between the two are, and will be able to move from voicing to voicing without counting frets.
To play the last major chord voicing above, you again have two options. You can find the root note on the 5th string, and form the chord around that note. Alternately, you can count up three frets on the 6th string from the last chord you played, and start the new voicing on that fret (ring finger on 6th string, middle finger on 5th string, index finger on 4th string). This third major chord is referred to as a "second inversion" major chord. If you would like to bring these voicings full-circle, count up five frets on the sixth string, and play the root position chord again. Once you've memorized these chord shapes, try moving back and forth between all three chord voicings for the major chord you've chosen. They should all sound similar; all three chords shapes above contain the exact same three notes. In each voicing, these three notes are just arranged in a different order.
Example: to play an Amajor chord using the above 6th, 5th, and 4th string voicings, the root position chord starts on the 5th fret of the 6th string. The first inversion chord starts on the 9th fret of the 6th string. And the second inversion chord starts on the 12th fret of the 6th string.
5th, 4th, and 3rd String Group Major Chords
If you take a quick look at the above diagrams, you'll notice they are exactly the same shapes as the previous chords formed on the 6th, 5th, and 4th strings. So, follow the above rules for these chord shapes, and you'll have learned three more ways to play a major chord.
Once you're comfortable with the above chords on string groups 6,5,4 and 5,4, 3, try using these same shapes to play different major chords (eg. F, Bb, E, etc.)
Example: to play an Amajor chord using the above 5th, 4th, and 3rd string voicings, the root position chord starts on the 12th fret of the 5th string. The first inversion chord starts on the 4th fret of the 5th string (or the 16th fret). And the second inversion chord starts on the 7th fret of the 5th string (or the 19th fret).
Once you're comfortable with the above, try moving on to the two remaining string groups.
