How do you teach chess to a beginner / rookie? Recently, I got some students (beginners) in chess, and I would like to teach them how to play but I don't know where to start! They already know how to move pieces and some concepts on how to play, but still they are rookies. Where can I start from ?
I have a couple of suggestions, some tried and true, others more experimental using modern technology.

1. Start from the endgame

Pros


Starting backwards will allow the player to understand chess at a deep, fundamental level
If you learn the endgame first, you are constantly moving toward a place you are comfortable with when you play the game (as opposed to a middlegame player, who is constantly moving away from his comfort zone)
The endgame is grounded on the concrete, but requires sound positional understanding to play well, thus learning it allows you to learn all aspects of the game 


Cons


It can sometimes be tedious to teach and learn the endgame (I'm having this problem myself)
It requires a lot of initial investment from the student, for what seems to be little return (they may get caught by tactics, or opening traps in OTB games, making them discouraged)


2. Teach a thinking algorithm

Basically, create a simple step-by-step process (allow the student to come up with their own and then help them tweak it) which aids in making decisions OTB (i.e moves). 

Pros


Very easy to do and has almost immediate results (an anti-blunder check at the end of every move goes a long way to improve one's game)
A fundamental skill which is necessary for every phase of the chess game
Can be built upon as more knowledge about the game is garnered


Cons


None, except for the fact that you aren't focusing on any one thing in particular


3. Tactics, tactics, tactics!

This is more experimental and involves drilling tactical puzzles (I recommend this book, the puzzles are beautifully arranged so that they build on one another) until they can be done "by hand" (i.e directly from memory). 

Pros


All the benefits that tactical training provides, including:

Able to handle complex positions with little difficulty
Increase in visualization abilities
Confidence in one's own moves (i.e that they won't be subverted by a missed tactic)
General decrease in blunders and increase in noticing opponents blunders

Memorization of the positions, allows the creation of "building blocks". These are useful because you can often simplify complex positions in these basic blocks
Its just more fun to explore tactical fireworks


Cons


Focusing on just tactics, does not give a true understanding of the game, which is really more important for future success
There is a diminishing return, after which no amount of drilling will help
It can be tedious