PHP brackets look like this:
<?php ?>
So with the breadcrumb code, it would look like this:
<?php if(class_exists('kclass_breadcrumb')){ $bc = new kclass_breadcrumb; } ?>
There are a few files you can add this to, for individual posts it's single.php / for individual pages it's page.php / for archive (category) pages it's archive.php. Where you want to place the code is up to you, it needs to be outside the loop:
if (have_posts()) : while (have_posts()) : the_post();
otherwise it would show up for every individual entry (not a problem on page.php or single.php as only 1 article is displayed but in archive.php you'd end up with problems).