"That did seem a little over my head". Even if it's not over your head, it's definitely not worth the trouble.
• In the HTML editor, the code of a captioned image is like this:
[caption id="attachment_ETC ETC ETC ETC />[/caption]
If you weren't seeing this, then you were looking at the code of a non-captioned image.
• When you're about to insert an image, you get three options as to what happens when a visitor clicks on it - see here:
http://wpbtips.wordpress.com/2009/04/26/images-the-three-link-options/
If you don't want the images to be clickable (as I hoped), you select None.
• In that case the best practice is to downsize copies of your images in an image editing application to a resolution of 72 (which is what all browsers display) and the pixel width you really want on the post,*** and upload and insert these copies in Full Size. This way you don't waste your storage space, your pages load faster, and you get better quality as well - see here:
http://wpbtips.wordpress.com/2010/01/16/image-quality/
*** For the theme you're using, maximum width is 585px for non captioned images, around 550 for captioned images.
• So, if you want non-clickable images, and if the files you upload are no wider than 550px, the no dash business can be made easier:
a) Upload and insert the image without typing a caption in the Caption field. Switch to HTML. The image code will look like this:
<img src="URL HERE" alt="" title="FILENAME HERE" width="WWW" height="HHH" class="alignleft size-full wp-image-1234" />
(1234 is an arbitrary example, of course: each image will have a different number.)
b) Replace that code with this:
<div class="wp-caption alignleft" style="width: MMMpx;"><img src="URL HERE" title="FILENAME HERE" class="size-full wp-image-1234" /><p style="color:#666;font-family:Georgia;font-size:12px;margin:10px 7px 5px;">TYPE YOUR CAPTION HERE</p></div>
MMM should be WWW+14.
The commands I've added simulate the default captions of the theme minus the dash. If you wish you can make further changes as well (make the caption centered instead of left aligned, or change the size and/or the color and/or the font of the text). Let me know.