How to make a video of an iPad (or other tablet) screen
From what I recall 


The room should be dark, so the tablet is the light source.
Experiment with the brightness, but usually low is the way to go.
Camera doesn't need to be extremely close, but the more zoom you use the more obvious vibrations will be.
Put the DSLR in manual focus and adjust it so the tablet is just slightly out of focus - this will remove the moire effect.
You want a short depth of field. This is achieved with a lower F-Stop (larger aperture opening).


I attended a session by Hendrik Kueck (creator of Color Splash) at 360iDev on this topic specifically. It was called "Effectively using videos to explain and market your app". You can buy that video online for $3.50. It goes into a lot more detail and explains everything really well (and may even correct me on a couple points.) It is a deal at 10x that price.