Personally I've done it three different ways:
1. DVD recorder - I had one of those VHS/DVD combo thingies from Panasonic and it would actually record with composite video and audio (3 RCA jacks) input, though that is lossy in two stages (PS3 output and DVD recording) but it does result in video files on a DVD that you can then upload to YT. Doesn't look great but it's up to 480p and the sound is quite acceptable, and it was an inexpensive option at the time.
2. Video of TV - This is convenient if you have a nice phone or camera, but as UrieHusky said it's very important to get the perspective right and *don't move the camera or make any noise*. I had a gorilla tripod (the one that grips to anything) and a Canon camera that took decent video (considering I still had a CRT tv) and acceptable audio (surrounded by speakers).
3. HD Capture - I have a Hauppauge PVR, about $200 at Best Buy. Very good quality, easy to set up, easy to use, though you'll also need to get a PS3 component cable (5 RCA plugs) unless they make a PVR that has HDMI inputs now. Also you need to be sure your PC meets the system requirements. It's nice since it's not a capture card so you don't have to install it inside your computer (it connects via USB), but it is another box that has to sit on the desk somewhere.