How do you record what happens on a TV based video game like a Nintendo 64 while playing it without using a camera but rather directly recording what happens on the TV screen?

I would recommend using a recording device not a camera because the quality of the recorded picture might turn out slightly better. There are many ways to record the screen. You can use a dvd recorder, vhs recorder, hd pvr, or any digital recording device. I personally use a newelectronx hd pvr to accomplish this. Why did I choose this method, well because I also record retro games and the newelectronx hd pvr connects to both my Nintendo 64 and my playstation and xbox.

There isn't really much to using it. You connect the n64 to the hd pvr by the video and sound cables and then press the record button. If you want to view what you recorded then you don't need computer - just push the play button and viola the stuff you recorded pops back up on the same TV screen. It records and plays simultaneously as you play your video game so you can switch back and forth without hassle. Look around there are many recorders for this type of stuff - just make sure the one that you get can connect to the n64. See the related links for more info on this with pictures and videos.