How would you make a video like this?

I’m not an expert but it looks like they just used Flash to create it and then saved it as a vid file.

I believe it’s something; a type of animation, called “kinetic typography.” Someone here, I don’t remember who, identified it on an earlier question. You can find other examples here (though at least one of the links is dead or has been removed)

and a tutorial on how to do kinetic typography animations here. You can google the term and find more stuff on the process too.