You need to use filters to hook into manage_posts_columns and manage_posts_custom_column which will let you add the table heading and dates. The filters are slightly special as you need to include the name of your custom post type
manage_{$post_type}_posts_columns
manage_{$post_type}_posts_custom_column
where {$post_type} in your case is conferences
// Add the table heading
function conf_columns_head($defaults) {
$defaults['conference_date'] = 'Date';
return $defaults;
}
// Add the conference date
function conf_columns_content($column_name, $post_ID) {
if ($column_name == 'featured_image') {
echo get_field('conference_date', $post_ID)
}
}
add_filter('manage_conferences_posts_columns', 'conf_columns_head');
add_action('manage_conferences_posts_custom_column', 'conf_columns_content', 10, 2);
Untested code, but that should get you started.