Proteins are digested by the enzyme pepsin in the stomach, which only works in the presence of hydrochloric acid (HCl). (Note this is different from the acid in acid fruits, which impede protein digestion.) Different concentrated proteins require secretions of very different digestive juices, so one should only eat one kind of protein (and likewise only one starch) at a time. However, since most foods contain small amounts of protein, we ignore it in combinations, the rules for combining foods applying only to the concentrated starches, sugars, fats and proteins.
Starches, on the other hand, require an alkali medium and the amylase in saliva which contains ptyalin, an enzyme which breaks down starch into maltose. The process continues in the small intestine, where more amylase further breaks down the maltose into simple glucose, fructose and galactose. These are absorbed into the bloodstream, and taken to the liver, which dispenses the energy to whatever cells in the body need it. If there is no immediate requirement, the glucose will be converted to glycogen and stored in the liver, or into fat to be stored in adipose tissue.
So consuming proteins and starches together will result in each being impeded by the other. Similarly, the eating of sugars and acid fruits impede the action of ptyalin and pepsin, reducing the secretion of saliva, and delaying digestion. If insufficient amylase is present in the mouth (due to insufficient chewing, or too much sugar), any starches will not be digested at all in the stomach, instead clogging up the works until amylase in the small intestine can get to work on it.
Fats impede the secretion of digestive juices, and reduce the amount of pepsin and hydrochloric acid, so they should be avoided or used sparingly with protein-rich foods.
Vegetables and salads combine well with all food types.
Acid fruits clash with most things, so are best eaten on their own; melons also, a special case, which should never be combined with other foods. Sub-acid fruits are easier to mix with other types in moderation, but all fruits are digested not in the stomach but the intestine, so will just slow things down (and ferment) until they get there. This is why a purely fruit diet is so beneficial to health (especially when one is ill), there being no starches or proteins to impede the fruits which pass quickly through the stomach to the intestine.