The Inca unified, strengthened, and added to their empire mostly through peaceful means (but also through conquest as well). As a result, beginning from the current country of Peru, the Inca acquired parts of Ecuador, Bolivia, Chile, Argentina and Columbia.
However, I suppose "adding to" an empire isn't quite as specific as "unifying" it, so now we should speak about a unifying language, unifying roads, unifying religion, and unifying government.
First, the official language of the Inca Empire was Quechua, but there were many dialects spoken taking into account the nuances of the particular areas.
Second, the Inca considered their empire to encompass four regions or "suyus," with the central unifying force being the capital of Cusco. A grand system of roads was created to connect the capital with these four regions.
Third, the Inca encouraged the worship of their sun god whom they called "Inti." Further, they considered the Incan king to be the "son of the sun."
Fourth, as a result, the Incan government was unified under that one king considered to be a deity in himself due to his relationship with Inti, the sun god. The center of the government was this king (and the Inca family), and there were four provincial governments pertaining to the four regions of the empire.
Just a final note about peaceful acquisition, most of the regions simply allowed Incan rule. They would let the children of the ruling family go to learn about Incan ideas and governemnt, then the Inca would allow them to return in order to institute Incan rule. However, gaining the coast of Peru was not so peaceful, and the acquisition of that land was considered a "conquest."