Statistical compendia are the first place to look for statistics when you don't know who collects the information and you suspect statistics may be collected administratively (e.g., by a government agency) or regularly (e.g., an annual survey). Even if the compendium does not have the exact statistics you need, use it as a "guide to sources" and follow the source notes to the originating agency, where you are likely to find more information and statistics.
Like national statistical agencies, government agency and NGO and IGO web sites can be large and occasionally difficult to navigate, especially for the first time visitor. Also like statistical agencies, most government agencies and NGOs and IGOs have annual reports, yearbooks, or compendia. Look for these annual publications on the web site as a guide to available data. Below are just a few examples.
Most countries have agencies responsible for collecting national statistics. These agencies usually produce compendia similar to the Statistical Abstract of the United States. A good way to begin finding statistics for a foreign country is to identify the national statistical agency, then look on their site for their annual statistical yearbook or report.