The "bottom-fermenting" versus "top-fermenting" distinction is a conspiracy intended to confuse brewers!
Both ale yeast (allegedly "top-fermenting") and lager yeasts (allegedly "bottom-fermenting") work the same way. The yeast cells float around in the wort; when they bump into a sugar molecule they transport it through the cell membrane and metabolize it. They then excrete the waste products: alcohol (AKA "yeast urine") and CO2. The CO2, in and sticking to, the cells causes lots of cells to float to the surface forming krausen and yeast rafts.
Once the CO2 separates from the cells, the cells sink to the bottom, your fermenter fills with CO2, your airlock bubbles, and your beer becomes carbonated. Chilling the beer allows the liquid to absorb the CO2 better, separating the remaining CO2 from the cells.
Two of the differences between ale and lager yeasts is the lager yeast's tolerance for lower temperatures and their slower activity. Both lager and ale yeasts are active throughout the beer, but at some point someone said, "look at all the krausen on this ale. The lager doesn't have as much krausen. I guess the ale yeast is fermenting on the top and the lager yeast is fermenting on the bottom!"