Download the weather images from here
http://www.rrdownloads.net/
Weather.zip

Unzip the weather folder into the root of your RR install.
When done properly there should be a folder inside the RR root named Weather with image files inside. The full path is like this
C:Program FilesRoad RunnerWeather

Run RRConfig.exe also located in the root of your RR install.
Scroll to the bottom of the list and you will see "Weather Settings"
Set your City,State and Weather Units
example:
City,State=Chicago,IL
Weather Units=USA

Whatever skin you are using will need to support the weather function by including at minimum a WEATHER.skin file
If this file is not present in the skins folder its likely the skin doesn't support weather and you should either request this feature be supported from the skin author, create one yourself, or use another skin that supports weather.