How were previous civilizations able to fit and lift giant blocks with such precision?

Answer 1

It depends on exactly which civilization, since everyone did things a little differently. But, with questions like this, the usual answer is "Math and lots of experience".

There are some great examples of experimental archaeology (when archaeologists do an experiment to see if they can figure out how past people did something) from the internet and documentaries. A lot of these experiments involved things like rolling heavy stone blocks on wood logs or pulling sleds, using rivers/waterways for transportation and using counter weights to help with maneuvering.