The easiest way to watch YouTube on PS3 for CFW users is to install YouTube plugin for Showtime.
Is works nice and should satisfy most needs. But if you still need to use the official YouTube app for PS3 on a modified firmware, this might be a bit tricky. Go to TV/Video services section of the XMB, then open My Channels and select YouTube. It will prompt to install the app, confirm. After the app starts, it says “You are signed out of PlayStation Network. To use YouTube, you need to sign into the PlayStation network” and prompt you to log into the PSN. Using PSN should be avoided by most CFW owners. Fortunately, the YouTube app is just a web browser, and could be easily tricked into not using PSN. This is not so for true apps, like Hulu or Netflix or Redbox or any other streaming service. So navigate to the folder where the YouTube app is installed to your PS3 hard drive. Open the local subfolder and locate offline.html file. Usually it has quite some text inside, we need to replace it by one single line, which you may copy and paste:
<meta http-equiv="refresh" content="0; https://www.youtube.com/tv"/>
Save the edited file replacing the original. Now open the YouTube app again, and this time the PS3 YouTube app works without PSN access. When an update arrives, it may replace the file, so you will have to repeat the process. I checked this on the original version, 1.05 update, 1.09 update and the latest I could obtain YouTube app 1.11 update, and the method works. So go for it. You may install the app and the updates through XMB, or download YouTube app on the PC directly from Sony PlayStation network servers. Then just save the package to a thumdrive and install like a normal package. Please keep in mind that this is an official app, so if it doesn’t start on your PS3, only your hands growing out of your ass are to blame. You may be using a spoofer or something. Make sure you are using the latest CFW available, without any spoofers. Also the app may show a “Unable to contact YouTube” error. Maybe you are using an old YouTube app version, so update to the latest. Or maybe, your PS3 just can’t access the internet. So fix the connection, and watch my channel on the big screen.