Hi Melanie,
For the code that shows on your site you need to use textarea. More info on textarea if you're interested.
http://www.w3schools.com/TAGS/tag_textarea.asp
To make this simpler, I just copied the HTML code from the last link you gave:
<div class="content">
(not all code here, just pertinent section)
<p><img src="/sites/default/themes/mommy/images/125X125.png" /><br />
help us grow!<br />
<textarea class="link-me-textarea"><a href="http://mommybloggerdirectory.com" target="_blank"><img src="http://mommybloggerdirectory.com/sites/default/themes/mommy/images/125X125.png" border="0" /></a> </textarea></p>
</div>
In the HTML you need to find the div content area that this applies to e.g. in the example it is <div class="content">. Yours might not be a class, just something like <div id="somethinghere">.
You will need to set a textarea class as in the example <textarea class="link-me-textarea">. The textarea tag is what lets you put the code in there without showing an image.
Note the beginning <p> and ending </p> tags and the beginning <div>. The <textarea> and </textarea> beginning and ending tags. And make sure after adding any div's or classes that you add the appropriate ending </div> tags.
In your CSS file (example below is if you used a class - if a regular div, not div class, use a # before the named element [which I think you know

]) this is how she got the dashed box and set the parameters for her box. You can change settings to suit your needs.
textarea.link-me-textarea {
border: 1px dashed #51AED1;
font-size:8px;
overflow: hidden;
color: #EA7480;
background-color: #fff;
height:55px;
width: 170px;
margin-top: 5px;
}
textarea {
background-image: none;
}
I hope this helps and gets you going on this. Fun, eh?