* Library of Congress Classification (LCC): This system uses a combination of letters and numbers to represent subjects. For example, "J" is for Political Science, "K" is for Law, "Q" is for Science, and so on. Further subdivisions use numbers and more letters to get increasingly specific. This system is generally favored by larger research libraries and universities due to its capacity for detailed subject organization.
* Dewey Decimal Classification (DDC): This system uses a numerical system to organize books. For example, 000 is for Computer science, information & general works, 100 is for Philosophy & psychology, 200 is for Religion, and so on. Similar to LCC, it is further subdivided with decimal points to create very specific categories. This system is common in public libraries.
Within each main class (e.g., "Q" in LCC or "500" in DDC for Science), books are further arranged alphabetically by author's last name. There might also be geographical arrangement within subjects (e.g., books on the history of specific countries within the history section). Sometimes a library may incorporate a Cutter number to aid in further ordering books by author within the same subject.
Therefore, there's no single answer to "how" non-fiction is shelved, it depends on the library's chosen classification system (LCC or DDC) and its internal implementation of that system. However, the underlying principles of subject-based organization are consistent.