Since all of the previously illustrated major chord voicings have the same notes as a "normal" major chord, you could theoretically insert any of them at a time you were required to play a major chord. This is where personal preference becomes your guide; some guitarists will elect to use these shapes all the time, while others will use them more sparingly.
There are circumstances where these new voicings will certainly sound out of place. Assume you are the lone guitarist in a "campfire situation", accompanying a group of people singing. You would certainly not want to choose the A major chord shape on the 12th fret of the first string, amidst a bunch of other "normal" open strummed chords. In that situation, you'd want the full sound of open chords. If you were the SECOND guitar in that situation, however, the situation changes. In that circumstance, you could let the other guitarist play the open chords, and you could use some of these newly learned inversions. This would add a nice, fuller sound to the music. In any event, you'll need to let the musical situation dictate whether or not to use these major chord inversions.
How Do I Use These New Chords Effectively?
Learning the previous twelve shapes for major chords was the easy part. To start using these voicings to their fullest effect, you'll need to invest a good deal of practice time. A goal to set for yourself is to be able to move smoothly from one chord to the next in a progression (often referred to as "voice leading"). This will often mean moving from a root position chord to a 2nd or 1st inversion chord, a concept quite difficult to master at first.
The following example, Paul Simon's "Call Me Al", contains a nice example of these voice leading principles. It is also a perfect illustration of what you should hope to accomplish using these new voicings.
Did you get that? The progression moved from a 1st inversion Fmajor chord, to a 2nd inversion Cmajor chord, to a 2nd inversion Bbmajor chord. The sound of each note in each chord moving smoothly (and minimally) to the next in progression is very pleasing to the ear. Compare the previous example to the following:
Notice this doesn't sound nearly as effective. By simply sliding the 1st inversion chord to different places on the fretboard to play the appropriate chords, you've eliminated all the nuances voice-leading creates.
Before we move on, consider one last example. This uses the same progression, and also uses the proper principles of voice-leading. Yet, we've started the progression on a different inversion of the Fmajor chord, so it will again sound different than the other two.
This previous example represents an alternative set of chord voicings Paul Simon could have used for "Call Me Al". The voice-leading is strong, and the overall result is much more pleasing than the second example.
Practice: Play the above progression for "Call Me Al", starting on various inversions of the Fmajor chord on different string groups. This will lead to different inversions of each following chord, hence slightly different sounding progressions.
Phew! Got all that? Let's move on to the final step: Chord practice tips.

