Assuming what you’re after is both a logo and text, this would work – using a child theme as noted above you need to modify:
– the width of
<hgroup id="site-logo" class="clearfix">
(line 431 of header-extensions.php in the structure folder but do it in your style sheet) to accommodate both text and logo.
Then just before
<h1 id="site-title">
in the header-extensions.php in the structure folder you can drop in your image like this:
<img src="https://www.yourwebsite.com/logo.jpg" style="float:left;margin-right:20px;">
(Put your style for the logo in the style sheet, I’m just adding it in to show what I applied)