Hi Andrew,
Assuming that you’re using the default theme, you’ll need to manually edit the following file in order to remove the blog title and tagline.
/wordpress/wp-content/themes/default/header.php
I would strongly recommend creating a copy of this file before editing it, just in case something goes wrong.
You can edit this from within WordPress (if the file permissions on your server will allow you) by going to Appearance->Editor within the WordPress admin interface. Or you can edit the file with a text editor like notepad.
Basically you’ll want to find the following chunk of code in header.php:
<div id="header" role="banner">
<div id="headerimg">
<h1><a href="<?php echo get_option('home'); ?>/"><?php bloginfo('name'); ?></a></h1>
<div class="description"><?php bloginfo('description'); ?></div></div>
</div>
And delete or comment out the following two lines:
<h1><a href="<?php echo get_option('home'); ?>/"><?php bloginfo('name'); ?></a></h1>
<div class="description"><?php bloginfo('description'); ?></div>
Someone else might have a different / better solution, but as far as I can tell, this should do what you’re looking for without breaking anything else.