The Art of Translating the Rules
Everyone has their own way of learning. There's no blueprint to discovering the most effective way to teach your group new games. But with a few guidelines you should be able to condense the time it takes to get everyone on the same page. Just like recommendations, game selection and knowing the limits of your group is always a very important part of it. Not everyone has the patience to sit down and play a game where they have to remember a lexicon of keywords and hold onto a reference sheet as large as the game board.
Before even getting your group together, it's imperative for more complex games that someone reads the rules and thoroughly understands them ahead of time. Having to read the rules as you play, or read and then slowly translate piece by piece to your group will likely double the indicated play length on the box. Preparation is a big part of learning.
It's a lot of responsibility to be the teacher, because if you discover you've been doing things incorrectly it can fall on your shoulders. But with many games that I've had to teach or learn, the group is generally understanding that the first playthrough of most games can be written off as a learning exercise. We like to call it the "asterisk" game.
Where to Start?
Whether your game takes 120 minutes or 12 minutes, there's always one ideal place to start when teaching every game: the goal. Every game has a goal. And while not every game's goal is achieved in the same way, it's always best to start by defining the goal and working backwards. This way, every mechanic you teach from this point forward, will feel connected to the goal. The most common question people ask when learning a game is: "Why?" So start every session by answering that question, before it's even asked.
One Thing at a Time
If the game you are learning has extensive board setup, finish setting everything up properly before explaining anything. At the café, I make sure to have groups follow the setup page in the rules before I get into it. Not everyone can retain information being taught to them, while actively doing something else. It's important to have the undivided attention of the group so that key details aren't misheard or forgotten. There's nothing worse than playing a game of Avalon and having a loyal servant of Arthur throw in a Failure card on a Quest.
Additionally, be sure to incorporate mini-breaks in your "teach-flow", to allow for people's brains to process the information. Break elements of the game into logical sections, instead of jumping from mechanic to mechanic. For example, in a game like Seasons, spend one section describing how to properly read the cards such as the cost, the points awarded, when to apply its effects, etc. There's often a lot of information densely packed into a card - so it's important to make sure everyone can understand the language of the game.
Rules, not Strategy
Always limit any strategy talk when teaching a game. Part of the fun in learning new games is discovering the nuances. Feel free to give examples of how certain mechanics work, but don't give anything away unless it's a specific question being asked. Discovering combos and developing a playstyle is something that each individual should experience on their own. It's a naturally rewarding feeling when the game begins to click.
And above all else, be sure to exercise the utmost in patience. Nothing ruins a game session quite like the frustration of people not getting it. But it's normal for people, especially those who aren't frequent gamers, to be a little slower at processing instruction. As you get more comfortable teaching, you'll discover your own methods of guiding effectively. It's OK to get things wrong. At the end of the day, it's a game and the most important part is having a good time.