Mastering the Library's resources' does not mean reading everything in it, but being able to find items in the Library which will be useful to your studies. Mastery of the Library is best achieved by heavy use of the Library. Each course's syllabus will be a useful but crucially incomplete guide to what's available in the Library. Because syllabi must be incomplete and partial, you must also be able to find relevant material on your own. There are several strategies here, including the pleasant one of browsing along the shelves in a relevant section of the Library.
Serendipity can work.
But there are more purposeful strategies, too. Most scholarly books and articles also contain bibliographic information, so you can use what you are reading now to identify what you should read next. It is therefore very important to familiarize yourself with the main categories and subtle peculiarities of the Library's classmark system. A full 'guide' to the classmark system in American history will be circulated early in Michaelmas term. But the more you search for and find books, the more you will learn about the classmark system, and the easier it will become to find books in future.