Every screen that you want to fill will be on a separate layer. You will scale and position each layer to match the original footage. Then you will either need to mask the footage or create track mattes so the footage fits the screens. The screens will probably not be perfectly perpendicular to the camera so you'll probably have to use Corner Pin on each video you are using to replace a screen.
If there is any camera movement you will have to track the movement and apply the tracking info to the screens. If anyone or anything moves infant of any of the replacement screens you'll have to duplicate the background footage and do some rotoscoping of the object that passes in front of the screen so you can arrange the layers correctly.
To sell the shots you'll probably have to do some compositing of shadows and reflections on the video footage. It would really help us guide you through the process if we could see a still frame of the main footage.
All of this takes some skill and a pretty good understanding of how AE works. I would not attempt this in Premiere Pro unless you have a very simple shot with no movement and nothing more than some scaled and overlaid videos to build up.