WordPress: Programmatically publish a post (custom post type) with custom fields

// insert the post and set the category
$post_id = wp_insert_post(array (
'post_type' => 'your_post_type',
'post_title' => $your_title,
'post_content' => $your_content,
'post_status' => 'publish',
'comment_status' => 'closed', // if you prefer
'ping_status' => 'closed', // if you prefer
));

if ($post_id) {
// insert post meta
add_post_meta($post_id, '_your_custom_1', $custom1);
add_post_meta($post_id, '_your_custom_2', $custom2);
add_post_meta($post_id, '_your_custom_3', $custom3);
}