What are some examples of rain shadows?
The lee side of any mountain range.
A rain shadow occurs when moist air rises up a mountain side. As it rises it cools and eventually it cools to the point that condensation occurs (the cooler the air the less water vapor it can hold, or 100% relative humidity). As the air keeps rises more condensation occurs and the mixing ratio (the absolute amount of water in the air) drops (the relative humidity stays at 100%).
Eventually the air mass reaches the top and starts moving down the lee side. The sinking air warms, condensation stops and the relative humidity starts dropping (the air is no longer holding 100% of the water vapor it can). In this location because the relative humidity is dropping so much there is no precipitation.
In my part of the world we see this occurring to the lee of the Rocky mountains. This process also produces something called a Chinook, which is a strong warm dry wind coming down the lee side of the Rockies.