Start by breading it down. The square on the left can be created with one shape layer, stroke only and a trim paths animator added.
The Text on the left is a separate text layer. The square on the right with the text is easily created by putting a text layer above a solid or a shape layer and then using the text as a track matte. The line of text at the bottom is another text layer.
Parenting can be used to lock the left square and left text together and the right square and text track matte together. Then it is just a matter of setting in and out points, animating position and opacity. Really basic stuff.
Because you could not figure this out on your own I strongly suggest that you start here: Basic AE
Go through the first section completely, then dig into the middle and right sections to learn more.
By the way, the animated title would be a single composition. You would never edit all those shots together in After Effects. That is what Premiere Pro is for. AE should only be used to create composites, effects, and animations that you cannot create in your NLE. More than 90% of my comps are a single shot under seven seconds because most of the films I work on don't have very many longer shots in any of the scenes.
Thanks a bunch Rick, got most of it down!
One final question, near the beginning of his intro, the right box seems to slowly fade into the video before sliding to its spot, how did he manage to get that fade in effect?