* Peeling. I don't try to remove the dry peel, instead I just remove the whole outmost layer, comes off with a shallow cut then removing it. Yeah it's a bit of a waste, but often that first layer isn't in a great shape and you'd toss it anyway.
* Cut in half, place the halfs flat side down. Much easier to do the rest when it doesn't try to roll away from under you.
* Cut to slices without breaking the pack (i.e. keep it half-onion shaped). This is probably easier to do with a small knife than a large one.
* Cut the sliced packs orthogonally to previous cuts. Done, except if you want a tiny mush (in that case, use a bigger rounded edge knife, cut with a rolling movement so that the tip end of the blade keeps in contact with the board; same technique also works great for garlic).
As others have pointed out, you'll want a sharp knife (a knife sharpener is a good investment). Cut with sideways motion with a hint of downward pressure, instead of just trying to press down through the onion.
Additionally, a lot of people use a knife that is considerably too small for the task. I used to be one of them. It may look intimidating at first, but a bigger knife chops so much better!
you really want to use a proper chefs knife for all these tasks. The primary reason is that the knifes size and shape allow you to anchor it on the cutting board while making the cut. Having an anchor point allows you to make fast, precise and safe cuts. Another important point: Use a sharp knife. Dull knifes require much more force and are much more likely to slip - the injury risk is significantly increased.
* Cut both of the heads off.
* Peeling. I don't try to remove the dry peel, instead I just remove the whole outmost layer, comes off with a shallow cut then removing it. Yeah it's a bit of a waste, but often that first layer isn't in a great shape and you'd toss it anyway.
* Cut in half, place the halfs flat side down. Much easier to do the rest when it doesn't try to roll away from under you.
* Cut to slices without breaking the pack (i.e. keep it half-onion shaped). This is probably easier to do with a small knife than a large one.
* Cut the sliced packs orthogonally to previous cuts. Done, except if you want a tiny mush (in that case, use a bigger rounded edge knife, cut with a rolling movement so that the tip end of the blade keeps in contact with the board; same technique also works great for garlic).
As others have pointed out, you'll want a sharp knife (a knife sharpener is a good investment). Cut with sideways motion with a hint of downward pressure, instead of just trying to press down through the onion.
Edit: Forgot the first step.