How did the Inca unify their empire?
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."
The Inca were able to unify their vast empire thanks to many different factors and inventions.
First, they developed an amazing system of roads which allowed for fast communication throughout their empire. This road system was so well constructed it is still used today in some places.
Second, they had a very well structured government with the Sapa Inca, or emperor, at the top and several regional heads down lower. Religion also reenforced the structure by lending the power of the Gods to the authority of those in power.
Third, the Inca were highly militaristic. They used the power of their fearsome military to keep order and silence dissent. This military machine actually helped contribute to their eventual downfall since a civil war contributed to the factors that allowed the Spanish to take over their empire.