The conjunction и joins similar things. It joins compound subjects and
Сергей и Ольга работают здесь. Sergei and Olga work here.
Антон читает и слушает радио. Anton is reading and istening to the radio.
Вера студентка. И Таня студентка. Vera is a student. And Tanya is a student.
The conjunction a is used to indicate contrast between two things.
It joins things that are dissimilar.
Коля играет, a его сестра читает журнал. Kolya is playing, and his sister is reading a magazine.
Дом здесь, а аптека там. The house is here, and the drugstore is there.
The conjunction но is used to join two clauses, where the information
in the second clause is contrary to what is expected.
Look at this example in English:
I lived in Paris for one year, but I don't speak any French.
The expectation is that one should speak French after living in Paris for a year.
Она хорошо читает по-русски, но говорит ещё плохо.
She reads Russian well, but still speaks it poorly.