Instrumental case

The instrumental case has this name for a reason: any word in this case is become somewhat like an instrument. Let's look at some obvious examples:

Он копает землю (чем?) лопатой - He is digging the ground with a shovel.
Я поздравила брата (чем?) открыткой - I congratulated my brother with a postcard.
Она гуляет (с кем?) с подругой - She is walking with her friend.

In these cases, the shovel is an obvious instrument for work, postcard - "instrument" to congratulate a brother and friend helps to spend time, i.e. she also fulfills the functions of helpmate (roughly speaking, of "instrument").

In the case with the instrumental case, the first hint is the preposition С [s].
Я подружилась с одноклассниками - I made friends with my classmates.

Secondly, you should remember the usage with the prepositions of places: З, (behind), ПЕРЕД (in front of), ПОД (under), НАД (over).
Перед школой сделали фонтан - They have built fountain in front of the school.

And thirdly, there is a range of verbs which we often use in the instrumental case. These verbs are presented here according to the frequency principle, you can memorize them as a "pair" for a word in the instrumental case.

Быть (кем? чем? с кем? (где?) - to be (who? what? with whom? where?)
Стать (кем? чем?) - to become (who? what?)
Attention! We use the perfective verb in this example.

Являться (кем? чем?) - to be (who? what?)
Казаться (кем? чем?) - to seem to be (who? what?)
Считаться (кем? чем?) - to be considered to be (who? what?)
Называться (кем? чем?) - to be named like (who? what?)
Работать (кем?) - to work as (who?)
Гордиться (кем? чем?) - to be proud of (who? what?)
Заниматься (чем? с кем?) - to be busy (with what? with whom?)
Интересоваться (чем?) - to be interested in (what?)
Пользоваться (чем?) - to use (what?)
Руководить (кем? чем?) - to lead (who? what?)
Управлять (кем? чем?) - to manipulate (who? what?)
Болеть (чем?) - to have the illness (what?)
Бороться (с кем? с чем? (против кого? чего?) - to struggle (with whom? what?) (against who? what?)
Встречаться (с кем?) - to meet (with whom?)
Здороваться (с кем?) - to greet (who?)
Знакомиться (с кем?) - to get aquainted (with whom?)
Советоваться (с кем?) - to consult (with whom?)
Говорить (с кем? (о чём?) - to speak (with whom? about what?)
Разговаривать (с кем? (о чём?) - to talk (with whom? about what?)
Обсуждать (с кем? (что?) (to discuss (with whom? what?)
Спорить (с кем? (о чём?) - to argue (with whom? about what?)
Соглашаться (с кем?) - to agree (with whom?)
Гулять (с кем?) - to walk (with whom?)
Танцевать (с кем?) - to dance (with whom?)
Играть (с кем?) (to play (with whom?)
Ходить (с кем? (куда?) - to go (with whom? where?)
Поздравлять (кого?) с чем? - to congratulate (who? with what?)