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.