I can answer this as someone who works in modern manufacturing. During my formal education I had to make parts with tolerances of .001" using hand tools. This included hand saws, files and abrasive stones. These abrasive stones were known for quite a long time. Whet stones being a pretty easy example. Sand and oil was used as an abrasive for polishing armor, to the best of my knowledge. And polishing does involve the removal of very small amounts of material, similar to modern lapping procedures. So lapping and polishing could give you results in the .0001" range even by hand.

If anyone has better sources and better information, please shed more light on the subject. I am just citing what I learned in school and in my profession.

One of our earliest sources for this sort of thing is a books entitled On Divers Arts by a Benedictine monk named Theophilus. You can find a modern translation here: http://www.amazon.co.uk/Divers-Arts-Theophilus/dp/0486237842/

A more archaic translation, with the original Latin text is here: http://books.google.com/books?id=wo4EAAAAYAAJ&dq=%22An%20Essay%20upon%20Various%20Arts%20in%20three%20Books%22&lr&as_brr=1&client=firefox-a&pg=PA154#v=onepage&q&f=false

The short answer, is that bronze gears for clocks, at least in the 12th century, seem to have been largely hand-cut using a hardened steel file, a process that was ridiculously time-consuming, as you might imagine. I think other techniques using a gauge-plate were in existence by the 17th century, though.