Everyone has different ways of teaching new players or getting people into D&D. I've introduced it to many people and they have all loved it, even in the early stages of my DMing.
When it comes to finding to people to play a campaign, we all know that in it self is a mission. I tend to look for people who like to be someone else. Those who enjoy a game, not for the graphics or the popularity, but for the adventure and story. I explain to them that D&D is not just miniatures and stats. It's a grand story that can have more than one ending. I tell them that it is not preprogrammed so there are a multitude of ways of getting to one place. I explain how fighting can go from what they show in movies and video games to what their wildest dreams can show.
Once I know that they want to play, I teach them about building a character. I tell them in layman's terms what each stat represents and how it helps a character. I also give them scenarios of when they are used. If they have no idea where to start, I ask them how they play characters in video games. Do they like to hide and kill from afar? Do they find love in killing with magic? Or are they the type of person that goes in and Kills everything in sight? Then I give them rough drafts of characters. One of my favorite types of characters for beginners are the gestalt characters from danddwiki.com. It gives my players more options and a better balanced character. I also don't get too strict on rules. I just keep it strict enough to keep it fair and balanced. Plus, new players like the idea of being a little extra powerful at first.
Once they have their character (normally done a few days before our actual game day), I begin to weave the tale of how they met. I let them get into character by asking them to introduce their characters and give a short background story as to why they became adventurers. I start showing them the grid map and a bit about how everything works. I explain what dice to use and when. At first I will focus on encounters more than story so that they can get a feel for the character they have made. As we get together for more encounters, I start to push the story part more. I want them to want to come back just to here the what happens next in the story.
Finally, the players are hooked and begin to think like their characters. I always want my players to fall in love with their characters. I want them to try and keep them safe while fighting. I want them to feel the rush of risking it all just to save the world. It is this feeling that makes a D&D campaign great.
I would like to hear your ideas when it comes to getting new people and teaching them how to play. Feel Free to comment.