Yes, you can find some Web Designer demo movies on the Xara website.
There is also an example website at webdesigner.xara.com - this site was created in Web Designer and it is also an introduction to the product. You can find the document itself in the Designs Gallery of Web Designer in a folder called Introduction.
Gary Priester has written an introduction to the new features of Web Designer 9 on the Xara Xone (you can find a similar introduction to what was new in MX Premium v8, also on the Xara Xone).
We also have a Resource Index on our site which lists all movies and tutorials created by Xara and third parties, which you can either browse or search by keyword.