As you can see, the blog title is overtop of my graphics and the footer indicates "your name here". I also want to add more links - more than just "home" and "about".
Depending on the theme, blog titile is done when you go to the Dashboard. Go to appearance, header image and color, toggle text display to get rid of the blog title. You also control the sidebar through widgets.
Your links are probably coming from your style sheet . . . (the bold)
<<strong>li class="current_page_item</strong>"><a href="http://clearlygreendesign.com/blog">Home</a></li>
<<strong>li class="page_item page-item-2</strong>"><a href="http://clearlygreendesign.com/blog/?page_id=2" title="About">About</a></li>
As Garry said if you want to add to your footer, open the footer.php file and add the xhtml you want. Same with the header, open header.php and add what you want.
As for the index.php (at least the one in your blog root, basically all it does is bring up your header file. Not much to edit there.