One way to accomplish this is to create a new loop that pulls in the most recent custom post type, then displays its title and content.
<?php
$new_loop = new WP_Query( array(
'post_type' => 'YOUR_CUSTOM_POST_TYPE',
'posts_per_page' => 1 // put number of posts that you'd like to display
) );
?>
<?php if ( $new_loop->have_posts() ) : ?>
<?php while ( $new_loop->have_posts() ) : $new_loop->the_post(); ?>
<h2><?php the_title(); ?></h2>
<?php the_content(); ?>
<?php endwhile;?>
<?php else: ?>
<?php endif; ?>
<?php wp_reset_query(); ?>