Please remember that Google is your friend. I typed in wordpress + display random post and within seconds found the following
http://www.romantika.name/v2/wordpress-plugin-random-posts-widget/
http://www.bloganything.net/637/download-wordpress-plugin-random-post
There’s many more to choose from if those don’t suit you.
If you would like to hard code in template see Codex Random Posts
I know this is an old post but it helped me out a lot. Thanks guys.
Since this one’s still a little active. I’ve used
<?php
$rand_posts = get_posts('numberposts=5&orderby=rand');
foreach( $rand_posts as $post ) :
?>
<li><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
<?php endforeach; ?>
to get a rand post which works fine, as long as I choose to display the_title or the_excerpt (both, of course, text only). But if I choose the content, which are images, it doesn’t display anything. Could someone give me a hint why images wont show?
Thanks!