A way of seeing through the propaganda is what I would call realism-based-education. By that I mean reading "Public Opinion" by Walter Lippmann, "Manufacturing Consent" by Chomsky, and "Propaganda" by Edward Bernays, to start. Reading "The Prince" by Machiavelli would also be a good companion to these, though its focus is quite different. Reading these quick and easy to understand books has done more for my worldly education than going to college when it comes to building critical thinking.
People need to understand that mass media is for placing ideas into your head for the purposes of influencing future actions-- no more, and no less.