it depends on the theme. wordpress uses different 'themes' to layout the blog.
the easiest way would be to make a new image of the same size, rename it to the image being called (via view source) and overwrite the image on the server.
if they know some css, they can find the css file in /wp-content/themes/YOUR THEME NAME/style.css. in there, s/he could change the background: declaration for the header. again, it really depends on the theme once you get into editing files. replacing the image is the fastest path.
lots of info on the wordpress.org forums:
http://wordpress.org/search/change+head ... e?forums=1
and in the docs
http://codex.wordpress.org/Using_Themes ... _and_Fonts
will