The OECD has discussed methodology (in terms of OECD nations) in a number of its reports.
This includes How Was Life? Global Well-being since 1820 – which covers 25 nations.
They have also developed the Better Life Index- which compare well-being across countries, based on 11 topics the OECD has identified as essential, in the areas of material living conditions and quality of life.
UK government official measures of national well being and satisfaction. See the 2018 National Well being Index