From the WordPress Codex:
<?php
$the_slug = 'my_slug';
$args = array(
'name' => $the_slug,
'post_type' => 'post',
'post_status' => 'publish',
'numberposts' => 1
);
$my_posts = get_posts($args);
if( $my_posts ) :
echo 'ID on the first post found ' . $my_posts[0]->ID;
endif;
?>