There is no one-way of processing coffee, and the method selected by a coffee producer will be carefully considered and executed. The below summary is a very high-level simplification of complicated and fickle processes, and the methods continue to evolve. How a coffee is processed has a significant impact on how it will taste once brewed and in your cup.
The skin and pulp of the coffee cherries are dried in the sun, sometimes on raised beds, for several days/weeks, and then peeled off. During the drying phase the coffee bean will absorb flavours and sugars from the fruit, imparting a coffee with a typically heavier body that is sweet and smooth.
There is a tendency for this method to be used in countries that have limited rainfall so farmers can take advantage of reliable sunshine, and so that uncontrolled fermentation does not occur. This method is common in Africa and Brazil.
The skin and pulp are removed more quickly using fermentation over approximately a week, and then washed off before being dried. This method enhances the acidity of the coffee, and coffee processed with this method will be brighter, cleaner, lighter and fruitier. Common in Central America, parts of South America, Ethiopia and Kenya.
The skin is washed away, but the pulp is dried on drying beds without being washed. Over days/weeks the fruit is carefully managed to avoid fermentation of the remaining fruit, and results in a full bodied and sweet, while still light and fruity coffee. Coffee processed with this method will share traits of both the wet and dry process methods, being sweet and full bodied, while retaining acidity. This method is only effective in countries with consistently low humidity so fermentation does not occur. Brazilian farmers have excelled in this method, and it is also common in Costa Rica.