How did harpsichord and fortepiano players in the 16-19th centuries tune their instruments?

I think we have at least one harpsichord player among us. In the meanwhile:

How did they tune their instruments? There are some books that describe us how they were meant to tune, and there are some others that try to express tuning systems with mathematical expressions.

We find at first systems derived from Pythagorean tunings (from a sequence of 3:2 fifths), with some intervals adjusted (to improve whatever interval they didn't like, such as harsh major thirds). After a while we see people describing systems not derived from perfect fifths. In the 16th century we see a description of something that approximates what was later called quarter comma meantone temperament (the modern explanation would be defining the fifth from the pure major third). Those temperaments were then modified to get more and more useful intervals. By the 18th century we see circulating temperaments, those in which all diatonic scales and the chromatic scale can be used without some horrible interval getting in your way (however, not all major thirds were equal, and neither were all fifths and so on). Equal temperament is more of a 20th century thing, as far as I know. So, that covers the models. Were they standard in their time? There were at times different alternatives discussed in the literature... For a long while people were trying to solve the problem of making all intervals useful (compatible with each other), and many solutions were proposed.

How did they actually tune in practice? There were manuals telling people a sequence of steps. First, set this note to your reference. Maybe a pipe organ of known length, which would produce a known tone but is affected by changes in temperature. Maybe a whistle, which is not the most reliable thing. Tuning forks were invented in the early 18th century, and are also affected by temperature changes. Getting a pitch reference from another instrument could have been another possibility. Woodwind instruments were made in one piece in the Renaissance, so adjusting their pitch was not an option and people would have to tune to whatever they are made for. Were all references the same? Hell no. Surviving pitch references show us pitch has not been super standardized, not absolute at all. After having a reference you start setting some intervals pure, and then changing them (a little narrow, a little wide). The descriptions of those intervals are some times not so easy to get. Eventually beats were used to guide people (I think this is a 19th century thing, I am not sure), both as you want this third with n beats per second and as this third should beat as fast as this other interval.

I think it's safe to assume people changed tunings to their taste. We currently see that in middle eastern music, where you can find many interpretations of what a quarter tone is.

There are videos in youtube comparing different tuning systems. In some cases they sound pretty much the same, until some radically different systems are compared, or their worst intervals are shown.