Firstly you need to upload the image in question to your skin/images folder - either via ftp or through admin.
Then you need to find and open the template:
customer/right_bar.tpl
for your skin
Find the affiliates code, and below add the standard html code for an image and a link - but with the smarty code for the image path - e.g.
<a href="link goes here"><img src="{ImagesDir}/imagename.jpg" alt="" border="0" /></a>
You may want to enclose all of that in a div (layer) to align etc.
<div class="center">
code
</div>
Make sure you do have a class in your css file called center with attributes to center align the image if you wish.
Or change the name and add your own class with whatever attributes you need - borders, backgrounds, margins, etc.