That is fairly easy to do. Here is some info to get you started.
First, in your index.php file, look for the start of the loop. It will probably look something like this:
<?php if (have_posts()) : while (have_posts()) : the_post(); ?>
Before it, add this:
$post_num = 0;
And then right after, add this:
$post_num++;
Then all you have to do is add conditionals for adding different CSS classes. Since $post_num increments for each post, it will be 1 for the first. So you could do something like this:
if ($post_num == 1) {
do whatever for the first post
} else {
do stuff for the other posts
}
That will cover the index page. You can re-produce it for the search.php, archives.php, etc.
Hope that helps.