There are three major things going on in the video.
Firstly, there's just text builds going on, which is very straightforward. In this video it's not so much animated as just popping on and off in straight edits.
Secondly, there are some coloured linear wipes. Also very straightforward.
Thirdly, the magazine pages are animated using a camera flying over each page, also very straightforward.
All of these techniques are easily learnable, but I recommend you spend some time learning the basics of After Effects. Once you understand how After Effects works, most (or all) of the techniques in this video should be quite obvious to you.
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