The Web is a different creature from print media. While this may seem like a blindingly obvious statement, most graphic artists learned their craft before the Web. All too often print designers want to control the Web in the same way they can control print. It's a new medium—accept its differences. The most obvious difference is that you don't know what size window, which platform or browser, or even whether they're using an alternate user agent (e.g., a screen reader for the blind) to access your page. Most designers have acknowledged that sans-serif is the preferred type style for the Web and often use serif for headings or other large type.
But even in printing off the Web, designers are not back in their element because of the different nature of the Web. Yes, it makes sense to specify a serif typeface, replacing the Web's sans-serif (and switch to sans-serif headings if you wish). You may want to specify a new set of type sizes if the default results don't please you (but remember people with poor eyesight—anyone over fifty).
But now you have a standard 8½x11/14 page to work with. However, that doesn't mean that everything is back to normal. Anything laid out using tables is severely limited in its adjustment to print. For instance, A 1000 pixel wide table completely loses the right-hand side because there's no convenient way to adjust most tables. On the other hand, the current page, though trivial, displays at eighty percent of screen width but prints at full width on paper by adding a print CSS file.
New possibilities open up when you switch away from table-based layout. Often there's nothing in the left-hand column (the menu) of the table-based page that is relevant in print—but you're stuck with it unless you want to jump through some messy hoops, adding even more complications to your pages. Even printing in landscape mode doesn't solve all the issues. A more flexible design using a <div>/CSS-based organization would mean that many wide pages could easily be redesigned relatively painlessly to accommodate the width of a standard print page.
For probably more complete information than you want see
http://css-discuss.incutio.com/?page=PrintStylesheets.