How to identify which template WordPress’s default search-form retrieves in my theme

The file that is displaying the search result, is the search.php file from the main theme folder.

Below, you can find a working example that does the search of the default posts and pages:

'post_type' => array('post', 'page')

You can add a custom post in that array, for instance, if the custom post type has the ‘portfolio‘ name then add it to the array will be:

'post_type' => array('post', 'page', 'portfolio')

The whole search.php example:

<?php
/* The template for displaying Search Results pages.*/

get_header();
?>

                <!-- main -->
                <div id="main">

                <!-- intro -->
                <section class="intro">
                    <!-- search -->
                    <form action="<?php echo home_url(); ?>" method="get" class="search">
                        <fieldset>
                            <input type="text" name="s" id="s" value="<?php _e('Click or type here to search','text_domain'); ?>" class="text" >
                            <input type="submit" value="go" class="submit" >
                        </fieldset>
                    </form>
                    <p><?php printf( __( 'Search Results for: %s', 'text_domain' ), '<strong>' . get_search_query() . '</strong>' ); ?></p>
                </section>
                <div class="main-holder">
                    <!-- search results list -->
                    <section class="col" id="content">
                        <?php
                            $s = $_GET['s'];

                            $args=array(
                                'post_type' => array('post', 'page'),
                                'post_status' => 'publish',
                                's' => $s,
                                'orderby' => 'ID',
                                'order' => 'desc',
                                'paged' => $paged
                            );
                            $temp = $wp_query;  // assign original query to temp variable for later use   
                            $wp_query = null;

                            $wp_query = new WP_Query($args);
                            if ($wp_query->have_posts()) : while($wp_query->have_posts()) : $wp_query->the_post();
                                $thumb_url = get_the_post_thumbnail($post->ID, '', array('alt' => the_title_attribute('echo=0')));
                        ?>

                        <!-- article -->
                        <article class="article article-alt">
                            <div class="heading">
                                <h2><a href="https://wordpress.stackexchange.com/questions/261798/<?php the_permalink(); ?>"><?php the_title(); ?></a></h2>
                            </div>
                            <nav class="add-info">
                                <ul>
                                    <li><?php echo get_the_time('F d, Y'); ?></li>
                                    <li class="data"><?php the_category(', ') ?></li>
                                    <li class="data"><?php echo $cat_slug; ?></li>
                                    <li><?php comments_popup_link(__('0 Comments', 'text_domain'),__('1 Comment', 'text_domain'), __('% Comments', 'text_domain')); ?></li>
                                </ul>
                            </nav>
                            <?php if ($thumb_url) { ?><figure class="visual"><?php echo $thumb_url; ?></figure><?php } ?>
                            <?php the_excerpt(); ?>
                            <a class="more" href="https://wordpress.stackexchange.com/questions/261798/<?php the_permalink(); ?>"><?php _e('Read more ...','text_domain'); ?></a>
                        </article>

                        <?php 
                            endwhile; 
                                else: 
                                    _e('<h2>Nothing Found</h2>','text_domain');
                                    echo '<p>'.__( 'Sorry, but nothing matched your search criteria. Please try again with some different keywords.', 'text_domain' ).'</p>';
                            endif;
                        ?>

                        <!-- paging -->
                        <nav class="paging">
                            <ul>
                                <?php
                                    if(function_exists('wp_pagenavi')) { wp_pagenavi(); }                               
                                ?>
                            </ul>
                        </nav>

                        <?php
                            $wp_query = null;
                            $wp_query = $temp;
                        ?>

                    </section>
                    <!-- sidebar -->
                    <aside class="col" id="sidebar">
                        <?php dynamic_sidebar("Blog Sidebar") ?>
                    </aside>
                </div>
            </div>
            <!--/ main -->