First things first, where are you getting the content for the page from? If all the content you want to print is in a variable, than it is rather easy. Just use page.php?print=true to link to the printable version:
<?
$content = "...all your content for the page, but not including navigation links or logos or anything else...";
if ($print)
{
echo "<html><body><h2>MySite</h2><br />$content</body></html>";
}
else
{
echo "<html><body>...logos, nav buttons, etc...";
echo "$content</body></html>";
}
?>
Now this is a rather simplistic version, but it should show the basic concept. The important thing is to keep content contained in a variable. Another thing you might want to consider, once you get more comfortable with PHP, is to make a PDF version of the file. This is especially useful if the content is rather lengthy (breaking large amounts of text into columns in a PDF is far more readable than a web page).