While nothing is factually wrong with mrichich
's write up, I felt that the specific mechanics of the cooler could use some more clarifying.
On the outside the cooler looks like a large cube mounted on the roof. The sides are vented with the vents pointing down. The sides of the cube may be removed so as to get to the inner components of the cooler.
The removable side panels hold what are termed cooler pads. These square pads are made of either an organic straw like material that is bound together tightly enough to hold the square form, but with enough gaps to allow air easy passage. Or they are made from a uniformly designed plastic webbing type design. The plastic version costs more but lasts longer. The straw version will sun bleach over time and as the water wears away at the straw, it will become less capable of suspending the water.
The bottom portion of the cooler is a reservoir that holds water. There is a water flow control device almost exactly like the one you should find in the tank on the back of your toilet. Also located in the reservoir is a water pump that pushes water up to the top of the cube. At the top a splitter changes the one tube from the pump into 8 or more smaller tubes that run to the side panels, two tubes to a panel spaced equidistant.
The inside of the cooler is dominated by the blower. The blower pulls air through the pads then pushes it into the ventilation system of the house.
When up and running the reservoir fills with water that is pushed by the pump up to the splitter that then directs the water to the pads. Once it starts pouring into the pads the water drips down throughout the pad saturating it as the pads are designed to hold the water. Any water that doesn't get evaporated goes back into the reservoir at the bottom. The blower pulls air through the water soaked pads and sends it into the house.
It's also suggested that when running your swamp cooler that one cracks all the windows in your house. Coupled with a thermostat this is a relatively cheap way to cool ones house.