If you're referring to the actual shape of the laptop, the most straightforward way would be simply keyframing the paths (this looks like a shape layer to me, or something you'd make from a shape layer). Start by making keyframes for when it's all the way open, and all the way closed, then start filling in the middle (as needed) until the move looks right. Then add the lighter gray shape and do the same.
For the screen itself, I'd take the image or precomp that makes up the screen content, and use either the Corner Pin or CC Power Pin effect to match the perspective. There are ways to rig this kind of stuff so it follows the points automatically (it involves more complex techniques and/or some coding-like stuff called expressions) or you can just hand-animate that part as well.