I haven't spent much time in the HTML of my template (yet). However, I did want to know how to add a graphic as part of my header, perhaps a table with a graphic. There's a great solution I saw with a simple Google search which required only changing the template to NOT lock a template element. I wanted to know how to unlock template elements anyway, and I didn't want to actually modify the header widget in HTML file directly.
Anyway, I tried a work-around that doesn't require editing the HTML template at all. It occured to me that I could just put HTML where the header text would go. And, it worked.
When you edit your template (Dashboard > Template tab > Page Elements), click to edit your header. You can remove the Blog Description text completely if you like. In the Blog Title field, insert the HTML code for your image, with a 99-character limit, like <img src="http://www.example.com/banner.png" />
You should have, as a result, a header with a graphic in it. That's it. I still like the "unlock widget" method best, but this work-around requires no customizing at all.