Just in case before I explain how it works - I would like to say that am not a piracy advocate. There are thousands of videos which are legal to download and thousands which aren't. It is possible to download any video but please use your own judgement or check with the owner to save your self any piracy troubles.
Past that gibberish, iPOD any general or your iPhone supports mp4 format. iTunes recognizes the format and if a file is encoded as MP4 it will play the video.
Step I: Identify your video.
I will use a video from Coke Studio promo. By the way you are allowed to download the video from the coke studio website as long as you agree to their terms and conditions which are reasonable.
Click on the video and it will open in YouTube and copy the link in the address bar.(Click any picture for bigger size)
Step II: Visit http://keepvid.com/ and paste the link you have just grabbed.
Paste the URL copied from the YouTube addressed bar and pate it in the text box just before the DOWNLOAD button and the following prompt will come up.
Click "Run" and the following screen options come up.
Notice the option with MP4 and click the corresponding link to download the file as an MP4 file which can be sent to your iPOD in the usual manner like any other video file.
Step III: Cheers and enjoy your video. There is no step III.
It is possible to download file in multiple formats. 3GP is a popular format for mobile phones.In case you are interested in just extracting the audio - select the MP3 option and you are done.