To display the list:

Backlinks:

<ul>
<$list filter="[all[current]backlinks[]]">
  <li><$link /></li>
</$list>
</ul>

To make the $:/yourname/TiddlerLinkSummary template appear on every tiddler, you'll need to tag it $:/tags/ViewTemplate. Positioning it in the list is optional in this case, since it will appear after the listed items anyway by default.