"The harmonic thingy" means finding the twelfth fret, pressing the string lightly above said fret (just touch the string, don't press down) and then playing said string with your right hand. You'll get a high-enough pitched sound that the guitar tuner might be able to recognize it and tell you if you're sharp or flat.
By the way, considering the... fuzzy... g-string... *snicker*
This time the solution was to use the string tree. Does anyone have a recommendation for a buzzing A string that has no string tree of its own? My own old PJ has a tree spanning the D/G strings, but the A always looks like it's not angled enough towards the tuner.
Would cutting the A string a bit shorter and forcing less windings on the post help?