Slavery in the Aztec world was radically different from, say, Greek or Roman slavery.
When the Romans conquered a region and took men captive, they enslaved them or sold them to slavers. By contrast, the Aztecs invariably sacrificed the men that they captured in war. Women and children who were captured in war were likewise sacrificed on occasion, but they were far more likely to become slaves.
The basic unit of city organization was the Calpulli. The Calpulli can basically be described as a separate neighborhood where the individuals living within it were tied together by a community oriented social structure. Because of its community orientation, labor was organized through the Calpull and it was almost certainly compulsory. This made labor costs extremely low for cities, and basically eliminated the possibility of efficiently using slave labor for public projects.
The fact that men were not enslaved en masse and slaves were not used for labor intensive projects suggests that slaves were probably solely used for household or estate purposes. These would be menial tasks such as cooking, cleaning, grounds-keeping, farming, gardening, or functioning as sex slaves.
Although men were not (usually) enslaved through war, anyone could become a slave. Many slaves were poor freemen or women who sold themselves into slavery in return for food and some pay. In addition, people could be enslaved as a punishment for a crime and parents could sell their children as slaves.
Slaves were given some very significant legal protections in Tenochtitlan (the exact laws regarding slavery undoubtedly varied based on region and city), such as the right to marry, the right to own other slaves, and the right to purchase freedom. In addition, slaves could not be sold without their consent (unless they were deemed lazy by an authority), their children were born free, and they could not be beaten or killed arbitrarily.