What is the proper method for rolling paint on a wall?
You can apply the paint initially anyway you like, but to "finish" it you should roll up and down, moving the brush towards the handle side as you roll.  

The handle side gets the most pressure, so moving in the direction of the handle means that as you lap and overlap and overlap the paint moving along the wall, the lightest pressure is always the last pressure applied to the paint.  

This helps reduce the creation of those "paint lines" - ridges in the paint you see left behind if you move the brush away from the roller.

The downside here is this will tend to pull the brush off the roller over time, so you'll need to push it back into place from time to time.