Use the Genitive case to express 'of,' as in преподавђтель рџсского языкђ 'teacher of Russian, Russian teacher'. (Don't use an adjective here, because рџсский преподавђтель means an instructor who is a Russian.) Very often, the best English translation is an adjective + noun phrase:
преподавђтель истћрии a history professor
магазќн сувенќров a souvenir store
Use Genitive to express possession. For a-declension nouns referring to people it's better to use the special adjective in -ин for 's:
кнќга врачђ the doctor's book
Сђшина кнќга (= кнќга Сђши) Sasha's book
Мђшина кнќга (= кнќга Мђши) Masha's book
Genitive is also used to express certain other types of relationship between objects and people, where the best translation is, again, an adjective + noun phrase:
дљнь рождљния birthday (i.e., the day of one's birth)
реклђма пќва a beer commercial (i.e., a commercial 'related' to beer)
Дљнь танкќста Tank Driver Day (i.e. an annual holiday honoring tank drivers)