Start by identifying organisations that might be collecting the types of data you are looking for. Examples are: the International Monetary Fund for monetary and fiscal concerns, the World Health Organisation for health, the World Bank for development.
Remember that international statistics are dependent on the collection of data by national governments and other agencies, so the types, depth and dates of data are not always consistent between countries. Collection of data within individual countries also changes over time, may be inconsistent across states, and can be disrupted by events such as regime change and war.
Databases and websites provide searchable access to a great deal of publicly available data. However, some historical statistics and data may only be available in hardcopy sources. For historical statistics you should also search the Library Catalogue using a keyword search statistics and your topic e.g. population, and then refine your search to the historical period.
Australian digital research data.