I don't really understand the genitive case. Like at all. I don't know the genitive case pronouns, and even when to use it! Please help.
The main purpose of the genitive case is to show possession; it corresponds to the English possessive 's and the preposition of.
There's not much more to it than that: masculine and neuter nouns use des and add a -(e)s suffix:
Das Auto meines Vaters = my father's car
Das Dach des Hauses = the roof of the house
Feminine and plural nouns use der with no other change:
Der Mann seiner Schwester = His sister's husband
Der Hund der Kinder = the children's dog
As for genitive pronouns, they are not taught on this course because they are very seldom used in modern German. Their use is limited to a few prepositions that require the genitive case, but the dative pronouns are used in speech instead.
If you want to know how to make these pronouns, simply take the possessive adjective and add -er if there's no -er already:
meiner, deiner, seiner, ihrer, unser, euer, ihrer