(This is the original readme written by Jeremiah)

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Place the "WeatherIcon.php" file and the "WeatherIcon" folder
into your "\wp-content\plugins" folder, and then
chmod the "cache" folder inside the "WeatherIcon" folder to "777"
(if you didn't upload the "cache" folder then you can just create
an empty one in there and chmod it.)

**
Thanks to Beel there are 3 options
for the images: if you don't like the .pngs
in the wicons folder you can use the
"gif-wicons-black-background"
or the
"small-gif-wicons" in the alternate_wicons folder
just point it to the correct folder and
change your icon extension preferance from '.png' to '.gif'

Lastly, activate the plugin through the wordpress interface,
and add something like this to your template:

<?php if (function_exists('WeatherIcon')) : ?>
<li class="weather">Lufkin, Texas
<ul><?php WeatherIcon('KLFK'); ?></ul>
</li>
<?php endif; ?>

Change KLUF to your station code, and Lufkin, Texas
to a description of your location.

You can probably find your station code here: 
http://weather.noaa.gov/data/nsd_cccc.txt
or here:
http://weather.gov/tg/siteloc.shtml

You might also want to add something like this:

.weather_title { font-weight: bold; }
.weather { text-align: center; }
.weather ul li { text-align: center; }

to your "wp-layout.css" file.

--Jeremiah