A Mini Manual- As posted by Straith on the regular forums.

Is it snowing? Could a blizzard be ahead? Prevent bad weather with a Weather Control System, and try to reap the resource bonuses that various types of weather will bring you.

Seasons

The first thing to know about weather is that your empire goes through seasons. Starting with Spring, and ending with Winter, your empire experiences rain, sun, snow, and hopefully avoids extreme weather like typhoons, droughts, and blizzards. Each season lasts one real day.

Weather

Every real half hour, your empire's weather will change. If you choose, you can see which resource thrives on the current weather, and set more workers to gather that resource. If you have the same weather for too long, however, your condition can become 'extreme'. Too hot for too long, and you'll have a drought on your hands. Keep an eye on your weather meter, it will let you know if you're getting dangerously close to an extreme condition.

Weather Bonuses

Each type of weather creates bonuses and negatives to your resources. It's easy to spot if the weather is helping or hurting - check out your resources section on your 'My Empire' page. Each extreme weather type also effects resources.

Weather Control System (WCS)

With advanced research you will eventually be able to create a Weather Control System, which will help even out your weather. With a WCS watching over your empire, you will not suffer the ill effects of extreme weather, but you can still achieve all bonuses from nice extreme weather.

While a WCS will not guarantee that you'll never see a storm (for what healthy empire has no storms?), it will increase the odds of nice weather.

Watch out, however, for your WCS may be a target for your enemy, or you may choose to take out an enemy's WCS. If this happens, the target will likely experience an extreme condition.