How to display a sticky post inside a div?

You could simply follow the example from the Codex:

$sticky = get_option( 'sticky_posts' );
$query = new WP_Query( 'p=' . $sticky[0] );

The variable $sticky will hold an array of IDs, and you access the first sticky post via $sticky[0].

Then you need the WordPress Loop:

if ( $query->have_posts() ) {
  while ( $query->have_posts() ) {
    $query->the_post();
    echo '<div>';
    the_title();
    echo '</div>';
  }
}