I am only in my second year of Russian, but we have just started to study the accusative and genitive cases... So I might be able to help.

The way I have learned it, the accusative case is about the direct object.
книга
Я читаю книгу.

Where the Genitive case is about possession. The sentence that I was introduced to the genitive case was-
Я учусь в институте иностранных языков. I go to school at the institute of foreign languages.

иностранных языков is changed from Иностранные языки.

I don't know if I've helped at all, but that is all I know at the moment.