From anywhere, and everywhere. Economic historians are scavengers. 

I'm going to answer this with a focus on pre-1850, and split it into two parts, one part being Britain and the Netherlands and another for everywhere else, though note that the techniques for everywhere else can be applied to Britain and the Netherlands.  

Britain and the Netherlands

These two countries are in their own category because there's been an immense amount of research into them by quantitative historians, prompted mainly by trying to understand why these two countries in particular were the first to get so rich. 

The very first collector of national accounts, in the sense that developed into our modern concepts of National Accounting, was William Petty (1623-87), an Englishman himself. In 1665 he published a book Verbum Sapienti, which presented his estimates of population, income, expenditure and other such concepts in an integrated set of accounts for England and Wales. The objective was to help with mobilising resources for the second Anglo-Dutch war of 1664-7. Petty then went on to publish Political Arithmetick (1676), which compared the Netherlands with France, looking to explain why Netherlands, with a much smaller population than France, was performing so well economically. 

Gregory King (1648-1712) then published Natural and Political Observations and Conclusions on the State and Condition of England in 1696, which gave estimates of national income, consumption, and some figures on production.  The estimates were based on his work in the Herald's office, which gave him access to a wide variety of information about the upper classes in England, and as a commissionier for a new poll tax on births, deaths and marriages. King also had estimates of per capita consumption, public expenditure and revenue in England, France and the Netherlands in 1688, though the figures for France and the Netherlands were very rough. 

There were a number of other attempts to measure British national income in the 18th and 19th centuries, though they generally lacked crosschecks on measures of consumption and production. 

On top of this base of old statistical work, Britain and the Netherlands are the two countries that first saw the massive increase in the incomes of ordinary people. Therefore there's been a lot of work by historians digging up quantitative numbers to try to explain why the Great Divergence started here. Historians have spent years pouring over archives, putting together series on prices and production and wages, revising estimates and arguing over what really happened. 

Everywhere else

For everywhere else, historians do what they can. There are data sources that have survived, generally with large gaps, through the centuries. Figures on government expenditure and revenues, figures on imports and exports of goods (which often was recorded as customs duties were a source of goverment revenue), these tend to be more commonly found in more centralised countries. China even has official reports on harvests that Chinese officials sent to the central government. The trouble with these overall statistics is that to calculate a GDP per capita figure you need estimates of population. Okay, censuses are more common in history than the sort of estimates that William Petty and Gregory King did, but they were often irregular, and focused on things like military needs and taxation, so counting households rather than individual people. And they don't always exist, or survive, so estimates of population are often even rougher than those from censuses. 

There are other, non-government, ways of estimating total output, such as estimates of urbanisation rates - more people living in urban areas implies more production to move food (and in the larger cities, water) to said people. Estimates of land under cultivation - from both archeological studies (I understand that even flights above at the right time of day can produce shadows indicating old fields) and from commentaries of contemporary people who might note down that villages were being abandoned, or that more land was under cultivation.

Conversely, one can try to estimate consumption per person. A major resource for this is account books, kept by long-standing institutions such as courts, landed estates, monasteries, hospitals, universities, etc. These type of institutions typically recorded what they spent, on both commodities (eg wheat, wine) and in employing labour, both skilled and unskilled.  From this sort of data, historians can estimate wages of unskilled labour, then estimate the costs of a basket of consumption goods (eg bread, beans/peas, meat, clothing, fuel) over time and see how much the unskilled labourer could afford to buy. There are two limitations in this process - firstly typically we only have daily wage rates recorded for unskilled labourers, so we don't know how many days they were working a year, and secondly this misses that there might be compositional changes in the labour force that would affect GDP per capita. There are estimates of skilled labour prices too, but it is hard to control for differences in the skills, e.g. is a builder a bricklayer or a specialist in decorative stonework? 

Another way of estimating consumption per person is to look at inventories of assets in wills - if over time on average more and more property is being recorded that indicates that material wealth per person was rising. 

Methods arrived at by top-down approaches can then be compared with estimates arrived at by consumption per person approaches. Note however a limitation of this: GDP is a measure of production, not of welfare. During a war, a country can be outputing massive amounts of production in ways that don't translate to any economic improvement in the lives of the average person. For example, GDP in the USA and the UK surged during WWII, but individual consumption was suppressed by rationing and other measures, to free up resources for the war effort. 

Obviously all this is terribly rough and there are long-running disputes between various economic historians about what was happening where and when. 

Sources: 

Maddison, Angus. Measuring and Interpreting World Economic Performance 1500-2001. Review of Income and Wealth 51, no. 1 (2005): 1-35. doi:10.1111/j.1475-4991.2005.00143.x.

Angus Maddison,, Quantifying and interpreting world development: macromeasurement before and after Colin Clark Australian Economic History Review, Vol. 44, No. 1, March 2004

Historical National Accounting, Maddison-Project Working Paper WP-12, Herman J. de Jong and Nuno Palma June 2018, https://www.rug.nl/ggdc/historicaldevelopment/maddison/publications/wp12.pdf

What Makes Maddison Right?, Maddison-Project Working Paper WP-7, Jan Luiten van Zanden and Debin Ma, September 2017 https://www.rug.nl/ggdc/historicaldevelopment/maddison/publications/wp7.pdf

The Maddison Project: collaborative research on historical national accounts, Bolt, Jutta; Zanden, Jan Luiten. Economic History Review. Aug2014, Vol. 67 Issue 3, p627-651.