When you attend your classes in your second year at Hogwarts, your Professors will recommend certain books to be read as referential or supplementary material for class. While you do not compulsorily need those books to pass your class, you will find it more than helpful and interesting to go through those. You will come across all the recommended books in the current Hogwarts Library. If your Professor does not guide you to where the books are housed in the current Hogwarts Library, take a look at the "Textbooks" section of the current Hogwarts Library and you should stumble on them.

Of course, life at Hogwarts in your second year is not all about studying. There are also many amazing novels, student autobiographies, fan-fiction, poems and stories, books on interesting topics like wandlore, diaries and class-notes by various students, available in the library for those moments when you need fun and entertainment to refresh yourself or cure your magical exhaustion and when you need guidance. I have not made an exclusive list of books to read in second year at Hogwarts for you, because I found way too many books worthy of reading. I am sure you will find that it is the same in your case. So, don't forget to pay quick visits to the library to beat your blues or for counsel, whenever your like, in between the hassles of navigating your second year at Hogwarts.