Loaded question.
First, lets consider the components of a cheeseburger. The bun and veggies have a considerable percentage of carbohydrates, which are simply sugars and polymers of sugars. The cheese and meat patty have two classes of biomolecules- protein and fat. Each of these three biomolecules are acted upon differently in the process of digestion.
When you start to chew, an enzyme called amylase in your saliva starts to go to work on complex carbohydrates in the bun, breaking it down into simpler sugars. This is why a cracker, although salty, starts to taste sweet if you leave it in your mouth for a bit. Further, saliva lubricates the food, allowing your tongue to squeeze off a portion called a bolus, to be sent down your throat, where a flap of skin, the epiglottis, closes off the entrance to your trachea, so you don't choke to death.
Involuntary muscle contractions of a muscular tube called the esophagus massage the bolus of cheeseburger down from your throat down into your stomach. Thus, it's not just gravity pushing your food along, which is why you can eat (although I wouldn't recommend it) while upside down. The stomach is a muscular bag about the size of a hot dog when empty, but a boxing glove when full. The stomach is full of hydrochloric acid, which is strong enough to dissolve aluminum or iron, and etch brick. The strong acidity breaks down all the components of the cheeseburger into smaller, more manageable bits. An enzyme secreted by the stomach lining, trypsin, goes to work on the protein in the beef patty, breaking up the protein into its constituent building blocks, amino acids. All this is further enhanced by muscular contractions, shaking around this mixture, making digestion go by faster.
By the time the stomach is done, your cheeseburger is a soupy mess called chyme. It is squirted out of your stomach via the pyloric valve into the first foot of your small intestine. This region, called the duodenum, is a very interesting place. First, the chyme is very acidic, and must be neutralized by a base, in the form of bicarbonate (same stuff in baking soda) which is secreted by your pancreas. Further, your liver secretes bile, stored in your gallbladder. This bile is secreted into the duodenum to break up the fats from the cheese and patty grease into smaller globules. Remember- all this is happening in a water-based solvent, so fats won't dissolve, so some kind of a breaking-up agent is needed, and bile does this. Additional pancreatic enzymes, such as amylase, trypsin, and lipase further break down carbohydrates, proteins, and fats into microscopic particles.
The rest of the small intestine gradually becomes more suited for absorption, rather than digestion. The long, skinny tube of the small intestine is filled with microscopic projections, called villi, which increase absorptive surface area. Here, individuals sugars, amino acids, and fatty acids from the carbohydrates, proteins, and fats, respectively, diffuse through the intestine wall into the bloodstream, where you an use them. Since it is 20 feet long, a length specifically evolved to maximize nutrient absorption, the small intestine is coiled up very tightly in your lower abdomen. By the time it reaches the end, virtually all the nutrients have been absorbed.
The last part of the digestive system is the large intestine, a name that is slightly misleading. It is shorter than the small intestine, only about 5 feet long, but thicker. It proceeds from the the lower right hand side of your abdomen near your pelvis, up to right below your ribs, crosses over to the right side, and descends down to the left pelvis, and curves backwards. At this point, most of the nutrients have been extracted, so the large intestine serves mainly to absorb the water from the leftovers. This is why diarrhea is so dangerous- those involuntary muscular contractions that push food along are quickened, and water isn't absorbed as fast as it should, increasing the risk for dehydration.
Interestingly, your large intestine houses about a soda can's worth of bacteria that have evolved to form a symbiotic relationship with us. We give them food to eat, and, as their waste product, they give us certain vitamins, such as Vitamin K, that we can't get anywhere else. In people with lactose intolerance, the lactose sugar isn't broken down in the duodenum by amylase, so when the bacteria in the large intestine get it, they digest it, but expel carbon dioxide and other gas as a waste product, lending itself to the bloated feeling of lactose intolerance. Further, a round of antibiotics has the serious consequence of harming the bacteria here, which is the reason for post-antbiotic digestive symptoms.
By the time the waste is fully through the large intestine, it reaches the rectum, a storage facility for the brownish, semisolid waste, parts of your cheeseburger that didn't find use for you body. Assuming you topped your burger off with a good ser