Web browsers give you the ability to print the current page. You can trigger the print dialog box via javascript and you can use CSS to style that page such that the printed output bears little resemblance to what's shown on the screen, but that's about it as far as printing goes.
Going beyond plain html, you might be able to use something like flash, silverlight, or another browser plugin. But really the closest you can get is something like this:
<html>
<head>
<style>
@media print
{
.HidePrint { display:none; visible:none;}
}
@media screen
{
.HideScreen {display:none; visible:none;}
}
</style>
</head>
<body onload="window.print();">
<div class="HideScreen">
Page I'm printing
</div>
<div class="HidePrint">
Other content...
</div>
</body>
</html>