Copy the custom CSS into a text file and save as mystyles.css (or whatever).
Via FTP, upload this into the theme along with the other CSS files. (wp-content > themes > [your theme] > css)
Now add a link in your header.php file (or whichever file has the HTML head info) to call in that CSS, after all the other links. It should look like this: <link href="<?php echo get_stylesheet_directory_uri(); ?>/my_theme/css/mystyles.css" rel="stylesheet">
Alternatively, the Jetpack plugin from WordPress.com lets you edit CSS in exactly the same way. Just install it and paste your code in over there.