How do you get videogame footage onto your computer?

When I am on YouTube, I would see videos of people playing their games, and the picture is so clear on it. Obviously-- somehow-- these people got their gameplay onto their computer somehow (somehow...recorded it onto their computer). So...what I like to know is: how did they do it? I heard some things, like using a s-cable for the PS2, or something like that... Do you know how??