Add image to left of site title

I would like to add an image just in front of (left of) my site title. All hacks to header.php that I have so far found trash the site and do not work (or maybe I don’t understand enough to implement them properly).

Any help, explained very carefully, would be appreciated.

WordPress twenty eleven child theme is being used. It is a static site: https://www.w4npn.net Site title is at the very top of the cream-colored home page: Support Organization for…etc” Site is still being developed.

Thanks