how to video surgery

I find a really good way to learn is to take a video like this into After Effects and try to reproduce it.  I found it helped me understanding editing as well as the base effects.  Rick has pointed out how to do the circle zoom effect thing.  There's some good use of text animation in there too.   If you reproduce all the different steps, even in hand-keyframed ways, you'll increase your AE skills tenfold.

No shortcuts. Simply learn your programs as comprehensively as possible. Once you understand elementary techniques and basic workflows, you recognize them everywhere and often it quickly becomes clear that even seemingly complex videos are just based on consequent, repeated application of these principles. practice makes perfect, literally.

Mylenium

To figure out what is going on in any video you just start on the first frame and try and analyze what you are seeing. I didn't see one thing in your sample video that was not a layered shot. The first shot has a background video of a woman that could be a composite against a cloud. On top of that, there are at least two other copies of the same shot that have been masked with a circular mask scaled up, rotated, and repositioned. 

On top of that stack of layers, there is a text layer with the text on a circular path that is rotating, another text layer, and a layer with a single line. 

It sounds to me like you are very new to After Effects and the idea of composites. I strongly suggest that you open up the Learn workspace and spend 20 minutes going through the getting started exercises. Then spend a few minutes with the User Guide. This will give you the required skills and explain the basic workflow that allows you to create visual effects, motion graphics, and composites. It is also important to know that After Effects is not a video editing app. It is specifically designed to create composites and animations that you cannot create in a nonlinear editor like Premiere Pro.

No magic plug-in, just copies of layers, masks, and transform property adjustments.

The same goes for every other shot in the video. Nothing but layers, masking and animated position, scale, rotation, and opacity.