Digestion involves a large number of steps, mechanisms and enzymes so here I will just give a general overview rather than get bogged down in details.
The first step in digestion that many people miss is chewing (or mastication) which breaks food down in chunks that are more manageable. This gives the food a greater surface area to volume ratio which is very important in exposing as much surface as possible to enzymes to maximize the rate of breakdown. Amylase is also present in saliva and so in the chewing process mixes this enzyme such that long carbohydrates such as starch are broken down into disaccharide (made up from two smaller sugar molecules).
Once mastication has taken place the food is pushed down the esophagus is a ball-like form, often known as a bolus into the stomach where the acid not only kills any pathogens present but allows the correct pH for the enzymes secreted by the goblet cells to work. These enzymes involve pepsin that is an endopeptidase that is secreted in its inactive form that is then activated by the pH of the stomach. This endopeptidase cuts proteins in the inside of the polypeptide chain hence giving more "ends" on which an exopeptidase may act (exopeptidases remove an amino acid from the end and so the more ends the more digestion). So, with the churning of the stomach the bolus is broken down into a soup-like substance known as chyme which can then pass through the pyloric valve to the small intestine.
Once in the first part of the small intestine (the duodenum) the acid is neutralized to give a more alkaline pH that is optimum for the next set of enzymes. Bile is secreted after being made by the liver and stored in the gall bladder that emulsifies fats making them easier to break down my lipases. The pancreas secretes a variety of enzymes that break down the substances further, these include: the aforementioned lipase and more peptidase enzymes.
The jejunum is the next part of the small intestine and is responsible for the absorption of these digested molecules over the cell membrane and hence into cells. In order to maximize absorption the cells on the surface have long projections known as villi to increase the surface area. Following the jejunum is the ileum that serves to absorb bile salts and vitamin B12. This absorption step is very important as without it the digested food would be of no use as it could not be passed into the bloodstream and hence all around the body.
The large intestine does not digest the food any further and is mainly used in order to form faeces made up of the fibre that is indigestible to humans. Another important role of the large intestine is to house the symbiotic bacteria that can themselves digest some of the fibre; however more importantly they can supply vitamins to the host such as vitamin K.
Hopefully I have stressed how fundamental a process such as digestion is to humans and other higher eukaryotes as without it food could not possibly be taken into cells and so there would be no feasible food source.