The PSP is great for gaming, but using it as a portable media player can be a bit tricky. This is especially true when trying to watch a video online. The PSP browser is having difficulty with YouTube videos in particular.
Steps
Part 1 of 3: Use a Video Downloader Site

Step 1. Open your PSP browser
In the address bar, enter the following address: m.youtube.com. Don't forget to add the "m" to load the mobile site. This method does not require custom firmware or a pirated PSP.

Step 2. Find the video you want to download
It will not work with all videos. You will most likely get better results with videos uploaded before 2010.

Step 3. Move the cursor to the video you want to download
Press the Triangle button to open the menu. Click on "Address" from the menu.

Step 4. Double click Start
This will reload the page. In the address bar, visit a YouTube video download site. KeepVid is one of the most popular and is most likely to work with the PSP.

Step 5. Use the cursor to select the URL field
Press the Select button three times to bring up the History button. Click on it with your cursor.

Step 6. Click the URL of the video
In the history list, you should see the video URL at the top. Click on it with your cursor to place the URL in the field on the KeepVid site.

Step 7. Click the Download button to the right of the URL field
This will generate a list of download links for the video.

Step 8. Download the “High Quality MP4” file
This is the format most likely to work on your PSP. By clicking on the link, the file will automatically download to the VIDEO folder on your PSP.

Step 9. Close the browser
Navigate to the Video menu on your XMB. Scroll until you see your Memory Stick.

Step 10. Select your video
All the video files on your Memory Stick will appear in a list. Find the file you downloaded and try to launch it. If the reading fails, try downloading it with a different quality.
Part 2 of 3: Using a Hacked PSP

Step 1. Make sure your PSP has the latest custom firmware installed
You are going to need a hacked PSP running custom firmware to use this method. Any version of the PSP or PSP Go can be hacked.

Step 2. Download a homebrew program for YouTube
These programs can convert YouTube videos to a format that can be sent to your PSP, since it cannot normally play Flash files. The two most popular programs are: GoTube and PSPTube.

Step 3. Connect your PSP to your computer
Go to the Settings menu on XMB and select “USB Connection”. Copy the homebrew program file to the GAMES folder on your PSP.

Step 4. Press the Circle button on your PSP
This will disconnect it from the computer and you can unplug the cable.

Step 5. Start the program
Navigate to the Games menu on your XMB. Scroll down until you find the YouTube program you installed. Press the X button to open the program.

Step 6. Find the video you want to watch
Navigation varies depending on the program you have chosen. These programs will not always be able to convert the videos. This is especially true for new HD videos on YouTube.
Part 3 of 3: Using PSP2b

Step 1. Open your PSP browser
You don't need to install any particular browser. Go to the PSP2b site. The site is not really very reliable and might not work when you try to access it. If so, try again at a later date.

Step 2. Click on the link to start the search
Enter the terms you are looking for in the field or use the drop-down menu to select popular searches. Click on the Search button to start the search for videos.
Videos must be converted by the PSP2b service before they become available, so new videos may not yet be available

Step 3. Download the vLoader file
A link will appear at the top of the screen when you select your video. Use the link to download the vLoader file to your PSP. This file is required to play Flash videos on YouTube.

Step 4. Download the video
Once vLoader is downloaded, you can download the video you want to watch. You will have the choice between the High resolution version and the Low resolution version. You will have more success playing the higher resolution versions of the videos.

Step 5. Watch your video
Once the video has finished downloading, you can find it in the VIDEO folder on your XMB.