Symmetry.
To make a very flat surface plate, you can grind three less-flat surface plates against each other (three because if you only have two, the common surface guaranteed by symmetry can still have curvature). To make a very precise cylinder, you can grind a less-precise cylinder in a "V" formed by two flat surfaces. To make a very regular lead screw, you can grind a less regular lead screw with a less regular reversible nut. Now you can construct a micrometer, and from there your mill/lathe and you're off to the races :)
That's how you bootstrap precision, but taking precision from a basic form and putting it into a complex form is a whole other art. These days we use numerical techniques, but historically geometric construction would have been the ticket. For instance, take a string, use a "standard twig" or something to mark 3+4+5 sections of equal length, cut & tie it into a loop, tension it into a triangle with sides of length 3, 4, and 5 using the marks, and now you've got a right angle.
Modern metrology looks a bit different because time symmetry started beating spatial symmetry. Badly. Absurdly badly. Like "you get twice the digits for the same price" badly. You get 6 digits for pennies in a quarz oscillator and I know the metrologists have chased their clock stability out to at least 19 digits, probably more by now. Also, you can just transmit the reference over the air to globally coordinate accuracy for dirt cheap, you don't even have to ship blocks of platinum-iridium in inert atmosphere. Modern metrology is basically the art of "rebasing" other types of measurement onto measurements of time because time measurements are so ridiculously great.