One way to get exposure to Japanese culture is to actually travel to Japan. Unfortunately Japan's reputation, in the U.S. at least, is that it's horrendously expensive. In reality, it can be expensive, but doesn't have to be. James Liu's travel guide that was formerly listed in this section no longer appears to be available.
Nothing can substitute for a well-written paper guide book, however.
The most egregiously expensive part of a trip to Japan is probably, in the editor's opinion, transportation, so plan your itinerary carefully in advance. A Japan Rail Pass may or may not be a profitable purchase. Finally, although English classes are compulsory in middle and high schools, many Japanese people speak little to no conversational English. Do not expect to get too far with English outside of large cities or popular foreign tourist traps.