How do you animate the labels for a diagram in Blender? I'm making this animation and the parts need to be labelled. 

This means that the lines from the label to each part will be animated and so will the text be animated.

two examples showing what I'm trying to achieve, here and here.

However, please remember that the lines will have to have an entrance in some manner. This is the context: 

This is the type of animations I wish for the lines: http://vimeo.com/27093074
Current .blend file.
To create animated lines like in the video you linked, you could use Curves and animate the start and end bevel factors. (see this related question)


Add a curve object
Set the Fill to Full in Object Data > Shape


Increase the depth in Object data > Geometry > Bevel:


Animate the start and end bevel factors by right clicking and selecting insert keyframe, or pressing I while hovering over it.


E.g. by animating the Start bevel factor from 1 to 0: