Instructions
Open your browser and download and install the YouTube Downloader program. The program is free and available on download sites such as downloads.com and others.
Go to YouTube and find a video you want to save. Then open YouTube Downloader. In the browser, copy the entire video URL by highlighting the URL in the address bar, right clicking your mouse on the highlighted text and selecting "copy." YouTube Downloader will automatically copy the URL into the "Enter video URL" text box. Click OK and the file will download into your selected download directory.
Click the dot that says "Convert video." This will automatically select the last video you downloaded for conversion. If you want to convert a different file click on the "..." next to "Select Video File" and select a downloaded YouTube video from your downloads directory. In the "Convert To" field select "PSP video" for conversion. Choose the video file quality you wish to convert and click OK. The file will now convert into a PSP playable file.
Mount your PSP portable by plugging the USB cord into the turned off PSP and the other end of the cable into your computer. Turn on the PSP and let the computer recognize your PSP.
Go to "My Computer." Your PSP should show up as a portable media device to which you can copy information from your hard drive. Double Click on the PSP drive and open a folder called "MP_ROOT." Under this folder is a sub folder called "100MNV01." Copy and paste the converted YouTube videos you want to view into this folder. Once the copying is completed, unplug your PSP from the computer.
View your videos on your PSP by navigating to the "Videos" menu from the PSP home menu. Your downloaded YouTube videos should be viewable on the portable device.