Many years ago (1987) my mom paid the mechanic at the local bike/ski/skate/hiking store (Bike 'N Hike in Albany, OR... yes they are still around) to teach me how to tear down, lube, and fix my bicycles. before that I had built single speeds and rebuilt a 10 speed my dad found in the dump (I was 17 at the time), but sometime in the early 90's my tools were stolen and I haven't replaced any of the bicycle specific tools. I can and will change my own tubes and tires, but that is about it anymore due to lack of tools and lack of space. I am sure there are plenty of books and internet articles on how to change component A or component B, but for me the best is getting hands on with a good mechanic (pay him for his time and have him tell you how to do a projects with you doing the labor).
I take my bikes to the local tire store and use their compressor to fill the tires unless I just need to top them off or I am in the field when I get a flat. I keep spoons, a tire gage, and a small patch kit in a bag under my seat when I ride and a small high pressure pump on the frame.