This might be a very good question for /r/askscience as well.

Early on, precise surfaces were generated by grinding, filing, lapping and scraping. None of these processes necessarily need modern, sophisticated machinery to perform.

Scraping, for instance, can produce precision of 0.0001" with nothing more than hand tools. With careful work, scraping can produce flat, square and parallel surfaces to high accuracy with no "modern" machinery or measuring equipment required. This is how early machine tools were built, and how some still are.

Additionally, machines used to be designed around a lack of precision. For example, the "Babbitt bearings" of old machinery did not require a precise fit between the bearing housing and the shaft within, since the bearing was cast around the shaft. And since old machinery was hand-fitted and did not require parts interchangeability 100% of the time, the tolerances would be looser to begin with.