It's really a pain in the butt on a PS3,
@Soren Jacquet. You need to have a "video capture card/device". Here is an external example:
Hauppauge HD PVR 2. You connect that device as an inbetween of your PS3 & TV via your computer. Once you have the video "captured" to your computer you can edit it and/or then upload it to YouTube. They aren't difficult to use, but like
@shaunm80 said, the PS4 is supposed to have direct exporting to YouTube, so unless you know you'd have a very good reason to get one now you're better off waiting.