About 'sharpening"; do you PUSH OR PULL the blade across the stone?

Depends on the stone. If it's a countertop wetstone, then you want to angle the blade slightly, while you pull and slide outwards. You never want a purely straight pull.

If it's a handheld micro-sharpener, then (while holding the blade at the sharpener designated angle) out and up, minding your fingers and wrist.

If it's a sharpening steel, there's a quite intricate motion that I can't quite describe in words, so I would suggest you visit YouTube.

For more on knife sharpening and diagrams, see: http://www.buckknives.com/about-knives/knife-sharpening/

To clarify on "pull" and "outward":

Pull means to pull the knife directly towards you, as if it were a rope in a tug-of-war game.

Outward means dragging left-to-right or right-to-left, as if drawing a line.

A pull-outward motion would be pulling the knife towards you while dragging it across the stone. This should create a diagonal motion that is heavily accentuated towards having more pulling movement than outward movement.

As noted in the comments, I am an advocate of pulling the sharp edge of the blade with the blunt edge leading, rather than the blade leading. To visualize, imagine a knife in your right hand on a stone. The sharp edge is nearest your left hand, and you move it across the stone towards your right.

Nothing clear here it seems to me. I have the same question.

Definition: 'push' means the edge moves such that it would cut into the stone if it were angled more.

'pull' means the edge moves such that it can never cut into the stone and the ground off residues are left behind on the stone.

My experience is that it doesn't matter. For the most part. And in the end you use both.

Doesn't matter because you are just removing metal. it is done equally well with a pushing or a pulling motion.

Then when you get to near the finish you'll get a fine 'thread' of metal along the edge that needs to be detached.

Going the 'other' way to that which you've been using will generally detach it more easily or quicker. I think. Very subjective. Just my impression.

Apart from the above I theorise that pulling back moves the metal over an abrasive slurry which cuts better than dry stone.

Pushing into the metal clears away the wet slurry to greater or lesser extent and would tend therefore to have the metal moving over dry or drier stone.

Hence I prefer to think that pulling back does a better job but I can't come up with any proof of this.

My sharpening research suggests that you want to use a motion that simulates a slicing motion like you were trying to slice off a thin peice of the stone. Depending on which side of the blade you are sharpening, it could be a push or pull direction.

I generally try to do it left and right.