Nice episode Ryan. I'm the guy in our group who always reads the rules and teach every one else how to play new games. I have the ability to get the game from only reading through the rules once, at least with most games. During our first game I do refer to the rules on setup (correct amounts etc.) and usually 1-3 times during the game.
People like it when I teach the game because I make it make sense. I go over the rules in a specific order. Usually I start with the goal of the game and what players must do to win: "To win the game you need the most points at the end, these things give you points". Then I usually give an overview of how the game works and then I go into detail of a player's turn and explain things in relation to the player's actions. My most famous (or infamous) line when teaching is "We'll get to that" because people are asking about things I'm planning on talking about later. If I start talking about various things here and there people will have a hard time following. If I have taught the game multiple times I know what people tend to misunderstand or mix up and so I pay extra attention on making sure people get these things. During the game I just let people ask questions, I really prefer open games where there are no hidden information so it's easy for people to ask about anything.