When do you use the German genitive to show possession?

The German genitive is used in a number of ways, but its number one use is to denote possession. This could be to do with anything, much like possession in English.

You can be really creative with the German genitive sometimes as you can use it to create long 'possession chains' - for example:

Das Haus der Freundin meines Vaters = my father's girlfriend's house (lit. the house of the girlfriend of my father).

In Northern Germany, the genitive is more common than in the South. Here they may be more likely to use von + dative, e.g. Das Haus von der Freundin von meinem Vater.