Place this code in custom.css, then change to your preferences:

/* Customize Previous and Next Links */
div.post_nav p {
color: #888888;
}

.post_nav a {
text-decoration: none;
}

On All Pages ∞

Place this code in custom.css, then change to your preferences:

/* Customize Previous and Next Links */
div.prev_next p {
color: #888888;
}

.prev_next a {
text-decoration: none;
}

Previous Link on Left, Next Link on Right ∞

Place this code in custom.css:

.custom div.prev_next p {
  float:right;
}

.custom div.prev_next p.previous {
  float:left;
}

On Single Post Pages ∞

Place this code in custom_functions.php:

remove_action('thesis_hook_after_content', 'thesis_prev_next_posts');
add_action('thesis_hook_before_content', 'thesis_prev_next_posts');

On Home, Archive, and Search Pages ∞

Place this code in custom_functions.php:

remove_action('thesis_hook_after_content', 'thesis_post_navigation');
add_action('thesis_hook_before_content', 'thesis_post_navigation');

Remove on Home Page Only ∞

Place this code in custom_functions.php:

function no_home_post_nav() {
if (is_home())
  remove_action('thesis_hook_after_content', 'thesis_post_navigation');
}
add_action('thesis_hook_before_content','no_home_post_nav');

Remove on Single Posts ∞

Go to Design Options > Display Options > Posts, and uncheck Show previous/next post links.