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I've been learning mandolin and one of the things that I have learned is that it is hard to remember what you have learned while trying to play. I learned some simple ideas that help keep some of this in my head. (from pickloser, mandoloin cafe)
two finger chords;
tiny: put your middle finger on g of d string(that is the head) then the 3rd of the chord sits on your left shoulder (b of the g string) the fifth sits on your belly button (d of a string) but also, since 5th is bigger than 3rd, 5th sits on right shoulder but one fret more away. The flat 7th is two frets from your head. There are more but these helped me the most. And I use them for violin also.
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Wow.
Isn't it strange how we all find "our own way" around music.... awesome !
I can't put my own understanding directly into words - but - I do know that for me it is all based on a basic understanding of the western scale and, in particular, the chromatic scale. Start anywhere, go up in steps of 2, 2, 1, 2, 2, 2, 1 ( semitone steps ) and you have a major scale, and so on for other scale types (pentatonic) or scale modes.
No - of course I don't actually "think" math when playing ( like the next semitone away is related by the 12th root of two or anything as specific as that ) - but that's where my own reasoning has come from. And knowing that we are tuned by 5ths apart on strings, it falls into place for me. My ear and its mapping to actual fingering (like 2-low etc - which I understand - but never consciously think about) also has a large part to play in this as well I suppose....
But no, I can't really put it into words..... probably because of the round-about way I came into music.....
I seriously recommend not copying my mistakes. D'oh - 
Please make your own, different mistakes, and help us all learn :-)
Using this "tiny" idea, put your middle finger on G on the e string and your index on the left shoulder (B on the a string) You have the G chord. Move both fingers up a string to C (on a string) and E (on d string) You have the C chord. Move both fingers up one more string each and you have the F chord. CFG. = 99% of early rock.
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