I had similar question in mind and to know the answer, I came to this forum. My actual question is how to teach 'Kids' chess and since it would be separate topic, I would post it separately.
I've taught some guys chess and I also start teaching with what's the objective of the game: capturing the King. However, I don't go too much into checkmate.
I'll start with how each power must move and I'll explain the unusual moves like 'castling' and 'En Passant' so that the newbie isn't confused when he/she see such moves. I'll then teach important factors like being cautious with 'FGH' pawns and then I'll then go more into Checks and checkmate.
I'm curious as to how different people prefer to teach the basics of the game to someone brand new that wants to learn how to play.
I prefer to start by defining the ultimate objective: Checkmate. I then explain the pawns and their various rules (captures on the diagonal, not forward... can only move one square except for it's first move, etc.), then get into the movements of the pieces... finishing with an explanation of three special rules: En passant, castling, and pawn promotion. If I feel they are getting overwhelmed by the initial description of the piece movements I'll skip over the special rules until later, and point them out to them as the situation develops in an actual game. During their first game I tell them beforehand that I'd like to play a "just for fun" game so I can point out various things as they arise, where I focus on their moves more than my own and can show various possibilities they have to choose from. After that I follow up with a second game where they are "left to swim on their own".
How about you? Is there a method or list you like to go through when you teach the game to someone totally new? My main concern is not overwhelming them and trying to ensure they walk away thinking what a fun game it is... making them enthusiastic to continue playing chess. Someone once did that for me, and I imagine most of us had similiar first experiences like that, otherwise we wouldn't still be playing!