It might be of interest to look at the table of contents of A COMPLETE CHESS COURSE by Antonio Gude: "... 3 Openings and Basic Principles 33 ... 4 Putting Your Pieces to Work 52 ... 5 Strategy and Tactics 76 ... 6 Endgame Play and Further Openings 106 … 7 Combinations and Tactical Themes 128 ... 8 Attacking Play 163 ... 9 Your First Opening Repertoire 194 …"
http://www.gambitbooks.com/pdfs/A_Complete_Chess_Course.pdf
Teaching my grandfather that’s never played chess before how to play.

Interesting whether the training for a senior should be much different than a child. I'd say the biggest difference is the evaluation of the game ending conditions: your grandfather should grasp quickly, faster than children do, that the piece movement and value is relative to the position (so the capability of mating the opponent or winning the same material back with interest).
In fact you could opt to start with the definite game ending conditions. So a win by checkmate (show the king and say that he needs to be trapped) or resignation (any color can end the game at will), or a draw by agreement; I'd leave stalemate and repetition for a bit later as that's pretty specific. Then show the starting position.
With that concept in mind, you can start explaining piece movement, relative piece value and center control followed by some basic opening principles and why you attack certain squares in the beginning.
Obviously
-How the pierces move
-The rules of captures, Checks, Checkmate, stalemate, draws etc.
-En Passant, castling, and promotion.
-Value of the pieces
-Forks, Pins, Skewers, and Discoveries
What else?