How was 6.02x10^23 determined for the number of fu/mole?
 

I'm just starting to relearn basic chemistry (high school was about 40 years ago), and I get that a mole for an element is a mass in grams equal to the number of its atomic weight.

Where does 6.02x10^23 for the number of formula units contained in any mole come from? Is this just an arbritrary BIG numer? Or is this somehow related to atomic number or atomic weight or some other physical property? How was this number determined (historically) or how would this number be determined with today's technology?

It's called Avogadro's number.

This http://gemini.tntech.edu/~tfurtsch/scihist/avogadro.htm seems to answer atleast some of the questions you're asking. Wikipedia also seems to have a page about it: http://en.wikipedia.org/wiki/Avogadro%27s_number

It's the number of atoms in 12.000... grams of pure carbon, I think.