You can use css to do this.
<img style="position:fixed;bottom:10px;right:10px;" src="YourImageURL" alt="Image title or similar"/>
You use the position:fixed property to ensure that your image does not move no matter what. You then set the exact positions you want the image to be in. In this case, the image is set to reside 10px from the bottom margin, and 10px from the right margin.
Position:absolute might also work for you depending on how your site is laid out. In other words, if you have a static site width, then you don't want your image fixed, you would want its position to be set with respect to the constraints of your site's content wrapper or container.