Drapes, if you tell us what your domestic DVD player is, we can tell you whether it supports any formats other than DVD Video. In any case, it won't include flv support.
You need a tool to grab the video off the web site. These are either computer-based, or web-based. Veoh is a web-based site that has just been sued by Universal, so expect all the other web-based services to disappear soon. There are plenty of capture tools on the computer side, for example "Orbit".
Once on your hard disk, the file will probably be the Flash .flv format, so you'll need to convert that to one of the MPEG formats. If your DVD player supports an MPG format, then you can stop there. Otherwise, you should check if your DVD burning software has a feature to convert & burn files. Failing that, you need a third-party tool. There's lots of them, too.
If you want to edit anything, Microsoft Movie Maker is hidden on your computer somewhere and does a reasonable job for free!