Photo by User:Colegota, CC BY-SA 2.5 es, https://commons.wikimedia.org/w/index.php?curid=773741
This wall is from Sacsayhuaman Cusco. We know why they built it this way—to withstand earthquakes. We do not know how. Here are some possible explanations:
Lifting stones is one thing Shaping them is another. How would the ancients make stone malleable? Shripad S. Akkivalli from India claims his father did it with an herb. There is a legend in Peru of using just such a technique. It was reportedly witnessed by a Catholic priest in 1983. That wall would take a lot of juice!
Basically, this means the stone was melted, and then presumably poured in place. The evidence for this is the glass-like (vitrified) finish on many of the stones.
We find vitrification all over the world. Indeed, in Europe there are many “vitrified forts.” (Experiments have been done and no wood fire is hot enough to vitrify rock.) We also have vitrified sand known as desert glass in Egypt, Libya, Australia, and Tasmania.
Guess, chip, and check
Of course the prevailing theory is that the ancients used a “guess, chip, and check” method on each stone, some of them up to 12 sided.
Here is a close-up of a wall at Sacsayhuaman:
Wikimedia-no attribution given