You can easily add elements to the sidebar of your site using widgets. In your case, you can use the Text widget to add a .gif file to your sidebar.
Go to Appearance > Widgets in your dashboard, then drag the Text widget into the zone where you want your blinkie to appear. Then, in the text area that appears, you will be able to paste the code for your image, like so:
<img src="http://example.wordpress.com/files/2009/07/boat.jpg" width="180" />
Of course, you will have to replace http://example.wordpress.com/files/2009/07/boat.jpg by the location of your image (for example http://www.theshabbyshoppe.com/images/blinkies/shabbyshoppe_blinkie_carousel.gif)
If you want to add a link to your image, simply wrap a link around that image code, like so:
<a href="http://www.theshabbyshoppe.com/scripts/homepage.asp"><img src="http://www.theshabbyshoppe.com/images/blinkies/shabbyshoppe_blinkie_carousel.gif" alt="" border="0" /></a>
Read more about using the text widget here: http://en.support.wordpress.com/widgets/text-widget/