These functions, if you are not familiar, create links to the previous and next post. They have many options but not one that lets you add a class to the link. If you want to do that, add the following code to your functions.php file:
add_filter('next_posts_link_attributes', 'posts_link_attributes');
add_filter('previous_posts_link_attributes', 'posts_link_attributes');
function posts_link_attributes() {
return 'class="styled-button"';
}For more on pagination, see Add Pagination to WordPress Templates.