If you want to add custom css on all the pages of a WordPress website except the homepage, you can do it via something like this. Put this code in the header.php of your theme file

In place of .yourcssclass you need to use your own css classes. This setting will work if you have a page set as front page from the reading settings.

In order to use custom css in some themes where homepage is not controlled by a page but from widget or theme settings, you can use