How do people create kinetic typography videos?

As others have noted Adobe After Effects is the gold standard for creating videos like this. However, if you don't want to spend a lot of money on the software and learn how to use it (there's a steep learning curve) I would highly recommend a service like http://videorascal.com (full disclosure, I'm the founder). Our system allows you to easily and cheaply create videos. You can view an example video below.

Adobe After Effects (AAE) is without doubt the most powerful and well known tool on the planet to create such animation. How do they do that? In principle, it's pretty easy. When you import an object to a composition in AAE, that object is assigned to a set of variables (i.e. position, rotation, scale, opacity, etc.) By manipulating the value of those variables over time, you can actually animate that object any way you want. However, to create the graphics, image or icons used in the video, Adobe Illustrator, Photoshop or Gimp (depending on what you prefer) are the one to do the job.

Professional explainer companies use adobe after affects for making explainer videos. Adobe After Affects is widely used in the making of explainer videos. You can also  use it for the development of Kinetic Typography. I am providing you with the tutorial link of Adobe After Affects on how to make kinetic typography videos. I hope that would help you to a great deal. Krestene John http://www.videoexplainers.com/

As you were already told, you need After Effects. Maybe the easiest way is to buy one of the ready-to-use http://videohive.net/search?utf8=%C3%A2%C2%9C%C2%93&term=Kinetic+typography&view=list&sort=&date=&resolution_min=&length_min=&length_max=&frame_rate=&category=after-effects-project-files&price_min=&price_max=&sales=&rating_min=&requires_plugins=&ref=altarvic  and change it.

Yep, After Effects is the way to go. We also create a lot of these type videos with no voice over at all- just the words and music. Some examples: Intel: Lionbridge: SuccessLab: NetApp:

It looks very nice but hard to do, but it isn't very hard at all. take a look at this article, everything you need to know about kinetic typography : http://www.designzzz.com/kinetic-typography/

After Effects, a nice music, cool fonts (not more than 2), a simple colour scheme and little bit creativity is all you need.