My study of amateur electronics began and ended with a Radio Shack 120-in-1 components-on-a-board project-kit. Specifically, it ended with the transistors. I never really figured out what they did or how they worked. (Although, I soon learned that if you ran 9 volts through one in a particular way, it would explode with a loud bang.)
If you know how a lightbulb works, and sort of understand what a capacitor does, then this page will probably help you understand transistors.