[Digital Jedi]

Well, first things first. Let's put the actual part people are going to click on to open the menu in the right place.

<!--Start Custom Drop Down Menu Part 1-->

<td id="custommenu" class="vbmenu_control"><a href="">Custom Menu</a>
<script type="text/javascript">vbmenu_register("custommenu");</script>
</td>

<!--End Custom Drop Down Menu Part 1 -->

vBulletin looked a little different when this tutorial was made in 2006, so it's not going to work under the first instance of <if condition="$show['popups']">. However, you've put it under the third instance. It needs to go somewhere under the second, otherwise it's incomplete table code just floating on the page somewhere. Let's put it in after/under the Calendar for right now:

<if condition="$show['popups']">
		<td class="vbmenu_control"><a href="calendar.php$session[sessionurl_q]">$vbphrase[calendar]</a></td>
		<if condition="$show['popups']">
<!--Start Custom Drop Down Menu Part 1-->

<td id="custommenu" class="vbmenu_control">
     <a href="#">Custom Menu</a>
<script type="text/javascript">vbmenu_register("custommenu");</script>
</td>

<!--End Custom Drop Down Menu Part 1 -->

(NOTE: That hashtag is important. Removing it will actually do the opposite of what you want it to do.)

You can put this pretty much anywhere you want, as long as you keep it inside the giant <table> that's containing all the menu items. Remember that it's a <td> cell, which means if you don't nest it properly, it won't look right. A proper table is made of the <table> itself, then table rows <tr> then row divisions <td>.

<table>
    <tr>
       <td>calendar</td>
       <td>custom menu</td>
       <td>new posts</td>
    </tr>
</table>

Everything neatly nested one inside the other. No overlapping tags.

Now the menu itself can go right where you had it. No one is going to see it until it's clicked on. But the code's a little mussy. The menu is a little table itself, with multiple rows <tr>, but only one <td> per row. Again, it needs to be properly nested to show up right.

<!--Start Custom Drop Down Menu Part 2-->

<div class="vbmenu_popup" id="custommenu_menu" style="display:none">
<table cellpadding="4" cellspacing="1" border="0">

<tr><td class="thead">Custom Menu</td></tr>
<tr><td class="vbmenu_option" title="nohilite">This opening row and cell
don't close in the right place, so they're not needed.

<tr><td class="vbmenu_option" title="nohilite"><a href="http://www.caught-the-skunk.com/index.php?pageid=new-york-supporters">NY Caught-The-Skunk.com Supporters</a></td></tr>

<tr><td class="vbmenu_option" title="nohilite"><a href="http://www.caught-the-skunk.com/index.php?pageid=new-york-fishing-flea-markets">Fishing Flea Markets</a></td></tr>

<tr><td class="vbmenu_option" title="nohilite"><a href="http://www.caught-the-skunk.com/index.php?pageid=new-york-fishing-boating-outdoors-shows">Outdoor Sports' Shows</a></td></tr>

</td>
</tr> This closing row and cell tag are not in the right 
place, either, and not needed.
</table>
</div>

<!--Stop Custom Drop Down Menu Part 2-->

Then when you get to styling it, just use the classes, as they're shown in the example. class="thead" for headers, and class="vbmenu_option" for the clickable areas. (Though a header can also be a link, if needed.) Hopefully, that get's you started on the right track.