Is there a way to take Screenshots from a DS?
Solution 1:
http://www.pressthebuttons.com/2010/07/isnitrocapture-yes-it-is.html
Hate to break it to you, but it's in the $3,000 range.
Solution 2:
Currently, no there is not. :(
However, you can get various NDS emulators for the PC, and take screens from those.
Solution 3:
There must be some means of getting video output from a DS, because G4TV and GameTrailers include gameplay video in their reviews, and there's no way they're playing the entire game in an emulator. And they're definitely not just filming the screen, because you can see effects of the stylus without seeing the stylus in front of it.
It's possible they have special hardware from Nintendo, or they may have in-house modders crafty enough to figure out where to solder a video cable to the motherboard. You might want to try asking on the GameTrailers forums how they record their videos of DS gameplay.
I also found this article on Nintendo DS on your TV, but it's really old (August 2006) and it says in an update that the device was a prototype that was never actually sold.