Nintendo never released any official video recording devices or TV-out for Nintendo DS/DSi/3DS, so it's either you mod the console, you film with a camera (or a cellphone, or a webcam, you get the idea) or you use an emulator. Unless you're an employee of either Nintendo or some gaming websites (they have officially modded consoles from what I hear) , there are no other options.
I ended up buying an unofficially modded 3DS with a capture card after attempting to record footage from my 3DS XL without modding. Audio capture is obviously very easy, but video capture is a pain when you use a camera, a cellphone etc:
EDIT: I forgot another thing I've seen on the internet: there's some sort of a camera attachment for the DS (you basically wrap it around the top screen of the DS), it doesn't require modding, but the colours are darker around the edges in the recorded footage and you only can record the top screen. I don't think these are available anymore, but just wanted to let you know.