Citizens of the Russian Federation: passport with registration and medical book.
Citizens of Kyrgyzstan, Kazakhstan, Belarus, Armenia: passport, registration, medical book, migration card with the purpose of entry "Work" (except for citizens of Belarus), СНИЛС, ИНН, ДМС (medical insurance).
Second citizenship: passport, registration, medical book, migration card with the purpose of entry "Work", SNILS, ИНН, ДМС (medical insurance). And also VNЖ, patent with checks or РВП for the city where you want to work.