For the population data, see Goldewijk et al. (2010) for the methodology used in version 3.1 (the latest version as of April 2011). The primary sources of historical population counts at the national level for HYDE 3.1 include:
World Atlas of Population History by McEvedy and Jones (Hammondsworth: Penguin Books Ltd., 1978) (see this post for the application of this data in economics research)For the data source of sub-national level population counts, see the description in Goldewijk (2005).
A Concise History of World Population by Livi-Bacci (4th edition, Oxford: Blackwell Publishing, 2007)
Used by Bluedorn et al. (2009) and Fenske (2013), the latter of which summarises how the data is constructed in detail on pp. 1369-1370.