OK. Hope I make sense here.
If we look at 3 string inversions. That means that u r using 3 consecutive strings to form the chord.
SO that means that we have 4 Groups of strings that we can use on a six string guitar.
group 1 - 1st,2nd,3rd strings to form the inversion chord
group 2 - 2nd,3rd,4th strings to form the inversion chord
group 3 - 3rd,4th,5th strings to form the inversion chord
group 4 - 4th,5th,6th strings to form the inversion chord
So lets start with GROUP 1 CHORDS.
The best way to learn inversions is to learn the shapes that make them up and to know where your notes are on the fretboard.
On the attached image the RED dot is the root note.
So all we do is learn the shape.
EXAMPLE:
If another guitarist was playing a G chord and u wanted to play a G inversion in string GROUP1 then this is what u would do -
If u find the root note (G in this case) on the 1st string then you would play an F shape (the middle image)
OR
If u find the root note (G in this case) on the 2ND string then you would play an D shape (the RIGHT image)
OR
If u find the root note (G in this case) on the 3RD string then you would play an B shape (the LEFT image)
SO if I want to play a G chord and I want to use the root note of G on the 2nd string (8th fret) then I play a D SHAPE so the fingering will be 1st string - 7th fret, 2nd string - 8th fret (our root note of G) and 3rd string 7th fret.
Darn I hope this makes sense.... it's so hard to explain something by typing....
check out this url for the shapes for the other string groups as well as minor chord inversions.
Its really easy once it clicks and they are really handy in almost all situations.
http://guitar.about.com/library/weekly/aa062401c.htm
gOOD lUCK
C