On the Komunitasweb.com blog there's a recent post walking you through the steps to add the Google weather content to your site, complete with icons.
If you need to show weather in your website, you can use weather widget such as weatherbug. It's nice and simple, but maybe you need something more integrated with your website. So, take a look at Google Weather API.
They use a SimpleXML object to pull in the XML data from Google's backend (as called via a URL) and loop through the resulting objects to output temperature, current conditions and several days of the forecast.