Fat digestion is a bit different than carbohydrate and protein digestion in that there are several processes that can occur in the digestion of fats.  The goal of fat digestion is to dismantle triglycerides into small molecules that the body can absorb and use.  Typically these are monoglycerides, fatty acids, and glycerol.

Digestion of fats....

Fat begins digestion in the mouth.  Some hard fats begin to melt when they reach body temperature.  The salivary glands at the base of the toungue release a lipase enzyme that digests a small amount of fat in adults but in children this enzyme very efficiently digests the short and medium chain fatty acids found in milk.  

On to the stomach

Fat does not do much in the stomach except float around in a layer above the components of other food.  Very little fat digestion takes place here.  The stomach is just a temporary way station for fat.  

To the small intestine

Fat enters the small intestine and a hormone is released that signals the gallbladdeer to release its stores of bile.  Remember that bile is produced in the liver from cholesterol that was carried there by HDL.  Bile is an emulsifier which simply allows the fat to mix with water.  Then the fats can be digested by the lipase enzymes from the pancreas.  According to some researchers, when you consider how fat is digested you can see the argument for food combining.