6th, 5th, and 4th String Group Minor Chords
The first step in playing these three voicings will be to find the root note of the minor 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 minor chord you're trying to play. You'll probably want to finger the chord as follows: pinky finger on 6th string, middle finger on 5th string, and index finger on 4th string. You're now playing an minor chord shape that you didn't know before. This is often referred to as a "root position" minor chord, because the root note is the lowest note sounding in the chord.
To play the first inversion minor chord, find the root note on the 4th string, and form the chord shape around that. Alternately, try counting up three frets from the note you played on the 6th string. This will be the starting note for the next chord shape. Plunk your fingers down (I might suggest middle finger playing the note on the 6th string, and the index finger barring the 5th and 4th strings), and you have a "first inversion" minor chord. 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 second inversion minor 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 four frets on the 6th string from the last chord you played, and start the voicing on that fret (ring finger on 6th string, pinky finger on 5th string, index finger on 4th string). 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 minor 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 Aminor 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 8th 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 Minor Chords
As was the case in the previously learned major chord voicings, you'll notice the above minor chords are exactly the same shapes as those 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 minor 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 minor chords (eg. F, Bb, E, etc.)
Example: to play an Aminor 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 3rd fret of the 5th string (or the 15th 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.