2d platformer physics

Ok, so I'm an intermediate game programmer, although not the best. Anyways I'm focusing on a 2D platformer currently and I'm following the " 2D smooth platformer" shown in this article http://goo.gl/0jE87H

So if I were to use an AABB how would I increment its movement based on the game time and not the FPS? I'm not exactly sure if I'm asking the right question since I am fairly new to this but as a more accurate desription I'm basically wondering if I increment its movement in a loop for example wouldn't that just move the character completely dependent on the processing speed of the device running it? If so what should I do to make it to where it runs at a certain speed? I already have the movement and jumping formula figured out.

I am also confused about how I would handle collisions (Like I said I'm not the best).

Thank you to all those who reply with helpful answers.