Most of the time all you have to do is link the site. Here is the code from NOAA's weather map:
<img src="http://www.nws.noaa.gov/forecasts/graphical/images/Tthumbnail.jpg" alt="Click here for latest NOAA National Weather Service forecasts of high and low temperatures and more in a graphical format." width="150" height="101" border="1">
example of what it looks like -
http://www.westga.edu/~stu9820/noaa.htm
I'm not sure about permissions but I'm sure is you put NOAA WEATHER FORECAST somewhere near the image it should be alright.