After looking at some sample pages of the Art of Electronics, I'm pretty sure the emphasis on heavy math is going to keep me out of that one for awhile. I guess that electronics learning kit at Radio Shack looks like the way to go, to start anyway.
It's funny, I did actually get one of those learning kits as a kid, and completed a whole bunch of the experiments, but I was approaching them from more of a "do cool stuff" mentality than a "learn why all this stuff is working the way it is" mentality.
Anyway, thanks for all of the advice, everybody.