Get the alphabetical sorted data with wpdb

It isn’t really WordPress-related indeed, but then again, OP doesn’t seem to know that, so here’s your answer :-). However, next time: this isn’t WordPress-related, please post PHP-questions in the corresponding SE.

Sorting a PHP array can be achieved by using the sort function, which sorts an array alphabetically by its values.

I’m assuming you have a one-dimensional array. If not, you should really edit your question with more information.

function thebook_get_provider_types() {
    global $wpdb;
    static $provider_types;

    if (! isset($provider_types)) {
        $row = $wpdb->get_row(sprintf('SELECT * FROM wp_postmeta WHERE meta_id = %d', CF_PROVIDER_TYPES));
        $provider_types = unserialize($row->meta_value);
    }

    // Sort the array alphabetically
    sort( $provider_types );

    return $provider_types;
}