I usually unintentionally introduce others to The Legend of Zelda games - typically kids. I just sit there and they watch me play. For example, my nephews like to watch me play Skyward Sword, and they ask a ton of questions about what's going on. With each question, I give them an informative answer which catches their interest. Which in turn makes them want to play it. I don't let them play my games, though; they're terrorists. lol Anyway, I was introduced to the series in a similar way. I was a little kid who liked to watch my older brother play A Link to the Past. I just picked it up and started playing, because it looked fun...
From my experience, I've found that it is much harder to get older people into the series. They typically ask many questions to which I can never provide an answer. Many of them question the logic of Zelda games. My brother's friends have asked such things as "How does Link place bombs in his bag when the fuse is lit?" (SS) But the most common questions are "Which is the jump button" and "Where to go next?" When I hand them the controller, they are completely clueless as to what's going on. There were also instances where newbies confused Link's gender. My sister has been the most difficult so far to introduce to the series. She's a bit of a tomboy, and she generally dislikes "adventure games where you have to defeat the wizard and save the princess." She'd much rather play a fighting game. It can be quite annoying, but when [if] they get the hang of it, it's pretty self-gratifying. It's a good feeling knowing that you've successfully introduced a new person to Zelda. Especially considering how daunting a task it can be. lol