Add a term to an attachment submitted from front end

media handle sideload returns an attachment ID, and attachments are normal posts with the post type ‘attachment’. All the same things apply, featured images parents taxonomies post meta etc albeit with a few attachment oriented functions like wp_get_attachment_image

So use wp_set_object_terms as you normally would, e.g.:

$id = media_handle_sideload(.... 
if(!is_wp_error($id)){
    wp_set_object_terms( $id, array(terms...), $taxonomy, $append );
}