This article describes how to get the URL of an image which can then be used in your contest page html code editor. Note that image URL's are protected and cannot be accessed directly from outside the contest domain.
Use one of the existing upload controls such as add image for a new logo in the theme editor.
Select "Edit" from the library thumbnails.
This will open the media item.
Select the image from the thumbnail.
Once the image is displayed, right mouse click and select "Copy Image Address". Note this can be displayed differently on different browser versions.