The methods for these kinds of studies vary from by place and period. I can give a brief-but-within-the-rules-of-the-subreddit account of early modern and modern Europe.

For early modern (and medieval to some extent) Europe, by far the largest body of sources for this kind of research are the vital indicators we can divine from the records kept by the Church: baptisms, marriages, and burials being the most important and corresponding roughly to births, marriages, and deaths. These kinds of records offer a potentially more comprehensive look at human population than censuses, tax records, and the very rare counts of births and deaths. The problems with both sets of sources are, of course, the same: records before about the 19th century are always spotty at best, and non-existent at worse.

The work in this field I know best is Michael Flinn's classic (read: chestnut) The European Demographic System, 1500-1820, which uses a technique called "family reconstruction." The researcher, using the records noted above, tries to trace as many individuals as possible through their particular family cycles: find their baptism, figure out when (if) they got married, how many children they had and at what ages, and when they died. If you can do that for many families over several generations, then you can get a reasonable demographic picture given the source limitations. Of course, this method loses a lot too: anyone who migrates is lost to the researcher; stillbirths or other pregnancies not carried to term are not counted; extra-marital relationships can slip through the cracks; and of course there must have been at least some individuals who evaded or resisted the gaze of the Church (see Le Roy Ladurie's Montaillou for a very old but extremely readable account of heresy in southern France).

And, of course, this approach is only even possible where local Church records are relatively good. Flinn suggests that, at the time he was writing in the late 1970s (yeah, it's a chestnut classic), something like half of all the studies doing family reconstruction were in France, and the records from "Germany, Italy, Switzerland, Spain, Hungary, the Low Countries, and all the Scandinavian countries" were sufficient to allow work that was "excellent" if not comprehensive. The rest of Eastern Europe was much more difficult to study, and both Ireland and Scotland had very poor records. At the point Flinn was writing, a handful had been done in England; less than ten years after he had written, Wrigley and Schofield published their comprehensive study, The Population History of England, 1541-1871, which used all of the methods to varying degrees depending on the availability of sources.

In the modern period, we are fortunate enough that governments began keeping much better vital records in the nineteenth century and have continued to do so through today. Dorothy Porter's work Health, Medicine, and the State is a broad overview of how governments have dealt with people's health in modern Europe; her work is a broader, empirical application of what Michel Foucault called "biopolitics" (The History of Sexuality vol. I; see also his Security, Territory, Population: Lectures at the College de France). Biopolitics is when the processes vital to human life become active concerns of the state. Porter argues, persuasively in my view, that the censuses and vital records that European states began to keep were crucial to how medicine and health worked. She notes that the local government in late 17th-century London began actively keeping track of births and deaths, and that all governments have intensified their data-collection ever since.

Finally, we should note the work of Floud, Komlos, Steckel, and more on stature. Roderick Floud (U. of Leicester?, see Health, Height, and History) got this kind of study started about the same time that Flinn, Wrigley, and Scholfield were working on demographics. But, instead of focusing on birth, marriage, and death, Floud (and a generation of graduate students) went looking for evidence of how tall people were at different points in their lives. The sources here were very difficult to locate, and if memory serves the first really good collection Floud found were foundlings who were packed off to the Royal Navy as 12-year-olds in the 1740s (they were like 4'3" tall or something, really quite short). But, data for this purpose gets better and more complete over time. By the late 19th or early 20th century especially, we have comprehensive data from public health inspectors in schools and the military, and it's merely a matter of legwork to reconstruct height at least for men--women are more difficult.

I hope that answers your question.