I finally figured it out, and here is how you do it:
Add the following HTML code to a HTML gadget (or "text" widget in Wordpress) in your sidebar:
<span><a title="Facebook" target="_blank" href="http://YOUR FACEBOOK PAGE><img width="100px" src="http://YOURIMAGEURL" border="0" alt="" /> </a></span>
<span><a title="Twitter" target="_blank" href="http://Twitter.com/YOURTWITTERNAME"><img width="100px" src="http://YOURIMAGEURL" border="0" alt="Twitter" /> </a></span>
The RED you replace with YOUR target page (for example, the URL to your facebook page or twitter profile).
The ORANGE you replace with the IMAGE URL that you want to show up.
The BLUE you replace with the size of the image you want.
This was always my confusion...what do you mean IMAGE URL?
The best and easiest way I have found to do this is to open an account at Photobucket (www.photobucket.com). From here you can download photos, and THEN it provides the links that you add to the code above.
If you like someone's twitter or social icon button, right click it and save it on your computer. Then, add that image to your Photobucket account. You can even resize it. Or, you can just resize it with the size in BLUE above.
I believe that with the particular code above, that you can have the image show up side by side, as well. Because my gadget is pretty narrow, they lined up one on top of the other.
On the right sidebar you can see how this looks if you use it in a wide gadget or a narrow gadget.
I hope this helps you!
CHICKY GROOVY COOLNESS GADGET