Adding breadcrumbs to a WordPress website without using a plugin can be done by creating a custom function and adding it to your theme’s functions.php file. Here’s an example of how to do this:

1. Open your theme’s functions.php file and add the following code:

function my_breadcrumbs() {
  
  $delimiter = '';
  $name = 'Home'; //text for the 'Home' link
  $currentBefore = '<li class="breadcrumb-item active" aria-current="page">';
  $currentAfter = '</li>';
  
  if ( !is_home() && !is_front_page() || is_paged() ) {
  
    
  
    global $post;
    $home = get_bloginfo('url');
    echo '<li class="breadcrumb-item"><a href="' . $home . '">' . $name . '</a></li> ' . $delimiter . ' ';
  
    if ( is_category() ) {
      global $wp_query;
      $cat_obj = $wp_query->get_queried_object();
      $thisCat = $cat_obj->term_id;
      $thisCat = get_category($thisCat);
      $parentCat = get_category($thisCat->parent);
      if ($thisCat->parent != 0) echo(get_category_parents($parentCat, TRUE, ' ' . $delimiter . ' '));
      echo $currentBefore . 'Archive by category ';
      single_cat_title();
      echo '' . $currentAfter;
  
    } elseif ( is_day() ) {
      echo '<li class="breadcrumb-item"><a href="' . get_year_link(get_the_time('Y')) . '">' . get_the_time('Y') . '</a></li> ' . $delimiter . ' ';
      echo '<li class="breadcrumb-item"><a href="' . get_month_link(get_the_time('Y'),get_the_time('m')) . '">' . get_the_time('F') . '</a></li> ' . $delimiter . ' ';
      echo $currentBefore . get_the_time('d') . $currentAfter;
  
    } elseif ( is_month() ) {
      echo '<li class="breadcrumb-item"><a href="' . get_year_link(get_the_time('Y')) . '">' . get_the_time('Y') . '</a></li> ' . $delimiter . ' ';
      echo $currentBefore . get_the_time('F') . $currentAfter;
  
    } elseif ( is_year() ) {
      echo $currentBefore . get_the_time('Y') . $currentAfter;
  
    } elseif ( is_single() && !is_attachment() ) {
      $cat = get_the_category(); $cat = $cat[0];
      echo '<li class="breadcrumb-item"><a href=""'.get_category_parents($cat, TRUE, ' ' . $delimiter . ' '). '</a></li> ';
      echo $currentBefore;
      echo get_the_title();
      echo $currentAfter;
  
    } elseif ( is_attachment() ) {
      $parent = get_post($post->post_parent);
      $cat = get_the_category($parent->ID); $cat = $cat[0];
      echo get_category_parents($cat, TRUE, ' ' . $delimiter . ' ');
      echo '<li class="breadcrumb-item"><a href="' . get_permalink($parent) . '">' . $parent->post_title . '</a> </li>' . $delimiter . ' ';
      echo $currentBefore;
      the_title();
      echo $currentAfter;
  
    } elseif ( is_page() && !$post->post_parent ) {
      echo $currentBefore;
      the_title();
      echo $currentAfter;
  
    } elseif ( is_page() && $post->post_parent ) {
      $parent_id  = $post->post_parent;
      $breadcrumbs = array();
      while ($parent_id) {
        $page = get_page($parent_id);
        $breadcrumbs[] = '<li class="breadcrumb-item"><a href="' . get_permalink($page->ID) . '">' . get_the_title($page->ID) . '</a></li>';
        $parent_id  = $page->post_parent;
      }
      $breadcrumbs = array_reverse($breadcrumbs);
      foreach ($breadcrumbs as $crumb) echo $crumb . ' ' . $delimiter . ' ';
      echo $currentBefore;
      the_title();
      echo $currentAfter;
  
    } elseif ( is_search() ) {
      echo $currentBefore . 'Search results for ' . get_search_query() . '' . $currentAfter;
  
    } elseif ( is_tag() ) {
      echo $currentBefore . 'Posts tagged ';
      single_tag_title();
      echo '' . $currentAfter;
  
    } elseif ( is_author() ) {
       global $author;
      $userdata = get_userdata($author);
      echo $currentBefore . 'Articles posted by ' . $userdata->display_name . $currentAfter;
  
    } elseif ( is_404() ) {
      echo $currentBefore . 'Error 404' . $currentAfter;
    }
  
    if ( get_query_var('paged') ) {
      if ( is_category() || is_day() || is_month() || is_year() || is_search() || is_tag() || is_author() ) echo ' (';
      echo __('Page') . ' ' . get_query_var('paged');
      if ( is_category() || is_day() || is_month() || is_year() || is_search() || is_tag() || is_author() ) echo ')';
    }
  
    
  
  }
}

This function uses WordPress conditionals to determine what type of page is being displayed and generates the breadcrumb trail accordingly.

2. Add the following code to your theme’s header.php file where you want the breadcrumbs to appear:

<?php my_breadcrumbs() ?>

This code checks to see if the current page is the front page (home page) and only displays the breadcrumbs if it is not.

3. Customize the HTML and CSS as needed to match the design of your theme.

With these steps, you should have a working breadcrumb trail that is generated without using a plugin. You can also modify the function to add additional conditionals or change the order of the breadcrumbs.