edit stylesheet for 1 page only

I am trying to edit a stylesheet for only 1 page. I do know what to edit thanks to Firebug, but any change I make affects other pages as well. I have tried to name this stylesheet with the page's name, but it doesn't make any difference.
My browser shows ..../index.php?main_page=checkout_payment for the page I am trying to edit.

The manual does not go into changing just 1 page, so I am at a loss. My guess is that I am either naming the page wrongly or I place it in the wrong folder.
Could someone explain the rules for that purpose (other than the read me CSS_read_me.txt located in the template-default)?
Thanks a lot!

just create a file called checkout_payment.css and put the changes in the file. Upload it to the CSS folder along with your stylesheet.css

All you need in the file are the specific changes to that page. Nothing else. It'll end up being just a few KB

The manual does not go into changing just 1 page, so I am at a loss. My guess is that I am either naming the page wrongly or I place it in the wrong folder.
It goes in your templates /css folder

Also there should be a readme that outlines per-page css
If not in yours look for it in /template_default/css

Thank you so much! I had tried different name versions, but not the correct one. :-)
Hope this helps other newbies like myself.
Thierry