Note that I do this from the computer. If you're doing it in real life, I'm sorry but I can't really help you there.
GameBoyAdvance: I use something called VisualBoyAdvance (or VBA for short). Open up "Tools" at the top then choose "Start .AVI recording". It'll now start recording but if the movie becomes 2 gigabyte or over, it'll become corrupt. I personally advice that you restart recording every ten minutes or so. I'm not sure, to be honest, how big they can be without it crashing.
Once done, open "tools" again and select "Stop .AVI recording". The movie is now complete.
SNES: I use something called Snes9x. Choose "File" and select "Record AVI..."
Every 4 minutes or so, the movie will automatically split (those movies gets real big real fast!) but it automatically resumes recording so don't worry. Also, do note that there is NO SOUND when recording. I don't know why that is, to be honest. It just isn't. You can listen to your own music, however, without it affecting anything. I've tried this twice myself and all you could hear was the game music in the finished movie.
Once done, select "File" again and choose "Stop recording AVI."
Congratulations, you're now able to record from VisualBoyAdvance and Snes9x! If you need more help (I don't see how you would need...) feel free to leave a comment.