as with anything there's many ways to skin a cat, but there's an example in wordpress docs here:
http://codex.wordpress.org/Template_Tags/get_posts
numberposts is the number of posts you want
orderby is rand which is equiv to mysql rand() which is random num
the docs show other parameters you can use also
i guess you could put this in page.php, although I guess it depends where you want it, etc, but i just posted general example
<ul>
<?php
$args = array( 'numberposts' => 5, 'orderby' => 'rand' );
$rand_posts = get_posts( $args );
foreach( $rand_posts as $post ) : ?>
<li><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
<?php endforeach; ?>
</ul>