The first stage of digestion occurs in the mouth. Mastication (chewing) breaks up the food into smaller pieces giving it a larger surface area for enzymes to work on, warms the food and moistens it with saliva. Saliva contains the enzyme amylase which begins the process of carbohydrate digestion. The food is then worked into a bollus (a small amount of food that can be comfortably swallowed) and the propelled down the oesophagus by peristalsis (rhythmic contraction of smooth muscles to propel contents through the digestive tract) and into the stomach.
The stomach acts as a churn mixing the food with gastric acids into a milky substance called chyme. The gastric acid lowers the pH of the stomach which activates the enzyme pepsin. Pepsin digests proteins breaking the links between amino acids.
Most digestion occurs in the duodenum but only small amounts can digested at anyone time. Small amounts of chyme are released from the stomach to the duodenum enzymes from the pancreas and gall bladder are added to the mix and the pH of the chyme increases to about pH 8. (i.e. the stomach acids are neutralised)
The gallbladder is a holding pouch for bile(produced by the liver). Bile works to aid digestion of fats (but note that bile contains no enzymes). Bile binds to fats to allow them to dissolve in the watery contents of the small intestine. This is called emulsification. Bile also helps neutralise the the stomach acids and raise the pH.
The pancreas actually has many functions, it produces digestive enzymes (for carbohydrates proteins and fats) but also produces insulin, the hormone responsible for regulating blood sugar. It also produces chemicals to neutralise stomach acids.
This is the second part of the small intestine (after the duodenum) digestion is still occurring and nutrient absorption begins. The small intestine has lots of small folds and villi (sometimes referred to as the brush border) which increase its surface area allowing a lot of absorption.
The third and last part of the small intestine is responsible for some very selective nutrient absorption such as vitamin C and B12. By the end of the small intestine most nutrients have been absorbed and mostly waste products and water enter the large intestine.
Large intestine (Colon) :
Here bacteria in the colon help with any remaining digestion of food (unfortunately bacteria digestion can produce some gaseous by products) . The mucosa of the colon has amazing absorption powers and water is recovered from the stool. Waste and gases are eliminated through the anus.