How do I identify a what kind of power connector for AC mains is on a product?

Look for IEC320 reference tables, the connector should match one of the international standards. Once you identify the connector you can search for it. If not, it is a custom cable and the manufacturer will need to be contacted.

The first edition of IEC 320 (later renumbered IEC 60320) was published in 1970. Source: Wikipedia

This is what a table looks like

Source: https://www.stayonline.com/reference-iec320.aspx

Edit:

Another good resource https://www.plugsocketmuseum.nl/ApplConn_overview.html

In addition to the IEC connectors @laptop2d listed, there's a few others that are also in common use.

Ceeform connectors are frequently used where high power and/or water resistance are needed. There's a whole series of them for 1/2/3 phase connections at different voltage and current levels.

Neutrik PowerCon connectors are also becoming more common, particularly on professional audio devices