You would want to put the css in one of the css files in your skin folder and then only paste in the html markup (just the parts inside the body tag, do not paste in a new body tag as the page already has a body) using source view of the editor. After making changes to css youneed to touch web.config to clear the server cache and you also need to clear the browser cache to get the new css. Some of the included skins already have corner rounding using this technique. This technique just can create a container with rounded corners it can't round buttons as far as I know.
Hope it helps,
Joe