How can I teach other people game rules?
Here are some things you can do. Keep in mind for the first game I'm usually more interested in teaching people how to play than winning, especially if I know the game well. This method might not work as well with a mixture of old hats and newbies.


Play with an open hand (maybe even have the other players do the same). This of course only works in games with secret information (card games especially). Make bad choices and explain why they are bad choices while you make them... especially if you can use those choices to illustrate points. So something like "Now I'm going to play Card X ... in a real game I wouldn't know (though I might guess) that you've got Card Y in your hand which is a perfect counter to my play."
On your turn explain why you are doing things, what benefit you might expect to get and how it would ruin everyone else's day. On their turns point out things they could do to make your life more difficult.
Take backs! Let them have them all they want where possible. Where chance is involved you might do a thing a practice time or two first so people can see how it works, especially if it's complicated.
If the game is complicated explain up front that you're going to parcel the rules out in digestible chunks. In Small world, I usually don't bother explaining going into decline until the second round. It's largely irrelevant to your strategy before then ... largely.


If despite all this you still win, that's okay, hopefully you've done a good job of explaining how you got there, and they'll trash you on the next game ...