middle finger on 6th string (low E, the fat string) if you let your finger straighten slightly it very conveniently mutes the 5th string which is what you want. This finger gives you the root note so the chord is determined by the fret where this finger is positioned, in our case we want to start on the 5th fret = A so chord is Am6, move it up 2 frets and you have Bm6 move up another fret and its Cm6 (so remembering just this one shape gives you twelve new chords that you know) first finger goes on 4th string ON THE FRET BEFORE THE ROOT (so if doing Am6 this is on the 4th fret) ring finger on the 3rd string on the same fret as the root note (in this case the 5th) little finger on the 2nd string on the same fret as the root note (in this case the 5th) high e string (1st string) is muted with the palm of the hand by just closing up the whole hand a little (or use whatever part of your anatomy works for you)

ring finger presses down the 2nd 3rd and 4th strings and also mutes the 1st string (it is easier than it sound) middle finger comes around the side and presses down on the 6th string and naturally tends to mute the 5th string (which is what you want) so only four strings actually sound, exactly what you need for a 7th chord (root, 3rd, 5th and 7th note of the scale for those into music theory)

Hope this helps, sorry if it is a bit long winded but I have tried to make it as clear as I can, I would hate anyone to be practising the wrong thing. Must be fretboard diagrams somewhere on the web but I have not found any nice ones yet.

Lastly there is a nifty little (free !) game at Fretboard Trainer