OKay, taking some guidance from here: http://support.advancedcustomfields.com/forums/topic/how-to-output-a-shortcode-in-an-input-field/
I did this:
<?php
global $wp_query;
$postid = $wp_query->post->ID;
$trailer = get_field( "trailer" );
echo do_shortcode("$trailer");
?>
Now it is outputting the shortcode from the custom field and printing it, but it does not execute it. I changed the Formatting for the field to No Formatting, but all it did is return the shortcode’s square brackets as HTML entities.