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Since YouTube.com is blocked, search for the video through a search engine like Google. One of the first links should be a link to that video's site on YouTube. There are multiple websites that allow you to download YouTube videos. Search for "YouTube downloader." Copy the URL of the video into the URL bar of the video downloader. Click the download button. The first time you visit a site that downloads videos, you will have to run a Java script. Only do this if you trust the site. Check reviews online to see if others feel the site is safe. It is possible that your network will not allow you to run the Java script when prompted. If this is the case, then you may not be able to download the videos at school.
Search for the video. Find a video download service.