i assume you have found loop.php ?
and the actual loop code showing the front page ?
and particularly the line <?php endwhile; // End the loop. Whew. ?> a few lines from the end ?
before that line, add your adsense code, ideally wrapped into a div with a css class for formatting; and definitively surrounded with some extra code; for instance:
<?php if( !$ad_shown ) { ?>
<div class="adsense">
<script type="text/javascript"><!--
google_ad_client = "pub-0123456789098";
/* adsense_ad */
google_ad_slot = "123456789";
google_ad_width = 468;
google_ad_height = 60;
//-->
</script>
<script type="text/javascript"
src="http://pagead2.googlesyndication.com/pagead/show_ads.js">
</script>
</div>
<?php $ad_shown = true; } ?>
be aware that this will now show adsense in most page with multiple posts – i.e. not only on the front page, but also in archives, search results, etc.
