I think it's important to makesure people understand what they are playing on the guitar and why they are doing things a certain way.
I gave my girlfriend her first lesson just the other day. She is already great on the piano (although she doesn't know much theory), and this was helpful to explain what's going on on the guitar. I began by getting her to work out some basic 'fretboard math' to understand the note relations on the guitar - how the same notes exist in multiple places etc. (5-0 tuning pattern, octaves, etc).
I'm teaching her songs of her choice, focusing on single note finger picking style things first, rather than chords. I think it makes a lot more sense to start with one note at a time rather than trying to fret uncomfortable open chords with untrained fingers.
I'm also making sure she understands proper fingering positions - being able to logically work out the best way to play a bar, relating to the bars before and after to minimalize hand movement and make use of all four fingers.
impressed with her understanding and ability in such a short space of time.