You Need:
- A PSP
- A USB cable
- A Memory stick for the PSP
- A free copy of Youtube Robot
Set up your PSP
Make sure you have your memory stick in the PSP. Plug the PSP into your computer with the USB cable. Turn the PSP on.Set the PSP to the "USB Connection" setting. From the HOME page (push the "home" button on the PSP), you will find it under the "SETTINGS" section.
Download Youtube Robot
It's a program that will capture the videos from Youtube and convert them into a form that you can watch on your PSP. Either visit their website, or Download the trial version right here.Use the program to download your favorite videos from Youtube by copying the URL from Youtube . . .

into the URL box on Youtube Robot . . .

Choose "PSP" as your format from the drop down box in the "Output Format" area.

Next, hit the "Tool" button on YoutubeRobot. Choose "Options", and look for a checkbox that says "Auto Convert After Download". It's third from the bottom on my version of the program. Make sure that box is checked, so the video converts automatically for you.

The video will be downloaded to the folder you select in the "Locate output Folder" area.

Hit the "Plus" sign to begin downloading.

Transfer the Video to your PSP
Here's the fun part. On your computer, in the "my computer" section, you should see an icon the represents your PSP. Mine shows up as an extra Hard Drive. Double click the icon to see what's on your PSP.You should see two folders on your PSP - MP_ROOT and PSP. Open the MP_ROOT folder.
Now you should see two more folders - 100MNV01 and 101ANV01. Open the 100MNV01 folder.
That's where you put the videos
But wait, you're not done with the last, and perhaps most important step. For some reason, you can put a perfectly fine video on your PSP, in the right folder, but if it is named anything other than M4V followed by 5 digits, the PSP won't recognize that it's there.
So, rename your videos to something like M4V00001 before transferring them to your PSP!!
Once you do that, they should show up under the "videos" section of your PSP, and you should be able to watch them on the go!