My first year Russian class was in high school. I was 16-17 years old. My teacher, who came from Leningrad, would bring his accordion to class and we would sing Russian songs, for example Подмосковные вечера, И кто его знает. We also had to memorize poems. I still remember some of Krylov's Волк и кот, http://er3ed.qrz.ru/krylov.htm#wolk-i-kot 40 years later.
I can pretty much pick up a book now and know where the accent falls, but there are still words that I would be unsure of.