for http://theeventscalendar.com/support/forums/topic/add-button-to-single-events-in-event-list-view/

functions.php

<?php
add_action( 'tribe_events_single_event_after_the_content', 'forum_1020203_custom_content' );
/*
  could use different actions to output to different places on event single page
  -- see /wp-content/plugins/the-events-calendar/src/views/single-event.php for more actions
  -- also listed below:
    tribe_events_single_event_before_the_content
    tribe_events_single_event_after_the_content
    tribe_events_single_event_before_the_meta
    tribe_events_single_event_after_the_meta
*/

function forum_1020203_custom_content() {
  $output = '<button><a href="#"></a></button>' . PHP_EOL;
  echo $output;
}