How to make a continuous sheet in MS Word?

To view the document as one continuous page without page separators:

Under the View tab switch to Web Layout. Note that your document's width will be "elastic" in this view, meaning your paragraphs will stretch to fill as much width as they are given (try resizing the window).

To change the appearance of the page separator in Print Layout:

Place your mouse pointer exactly on the separator line and double click. This toggles the display of white space between pages.

Double click to remove the space (replaced with small gray line) and the change your margins to custom and use 0" top and bottom. Looks pretty close to continuous. Otherwise the web view works as well (I don't like the width so I always manually change it to the standard 8.5" using Ctrl-A).