The instrumental case
The instrumental marks the means or accompaniment. It says how something is done or who is along with you. It's also the case for professions when used with the verb 'to be'.
Instrumental endings (singular)
Masculine: -ом / -ем. Стол → столом. Иван → Иваном. Учитель → учителем. Feminine -а: → -ой / -ей. Анна → Анной. Книга → книгой. Feminine -я: → -ей. Семья → семьёй. Neuter -о: → -ом. Окно → окном. Neuter -е: → -ем. Море → морем.
Personal pronouns in instrumental
я → мной. ты → тобой. он / оно → им. она → ей. мы → нами. вы → вами. они → ими. After prepositions: с ним, с ней, с ними.
Most common preposition: с
с + instrumental = with (in the company of). Я говорю с Анной = I'm talking with Anna. Чай с молоком = tea with milk. Don't confuse: с + genitive means 'from/off of', a different meaning.
Means / by what method
When you do something using a tool, the tool goes in the instrumental — without a preposition. Я пишу ручкой = I'm writing with a pen (lit. 'I write by-pen'). English uses 'with' here too, but Russian doesn't need a preposition.
Professions: быть + instrumental
In the past and future, profession nouns take the instrumental: Иван был врачом = Ivan was a doctor. Я буду учителем = I'll be a teacher. (In the present tense, where быть is invisible, you use the nominative as before.)
