Yes, learning the Library of Congress Classification system is not for the faint of heart. Fortunately there are some online resources that you can use to get a handle on how things are done in LC land.
The LC Classification system is a subject based classification system using alphabets and numbers to create subdivisions of a subject.
Classification Number Anatomy
Dennison University has a visual page that shows the construction of an LC number.
Another place to check is Tarleton State University Library has a clear tutorial page that explains how the call numbers are built.
If you have the current version of Java running you can access a Java based slide show on how the numbers function in the real world. First thing you will learn is that "Nothing comes before something" and the second thing is "single letters come before double letters." There is a quiz at the end to test your comprehension.
Theory Based Tutorials
Tulane University Howard Tilton LC Informal Notes page talks about the features of LC, how it was constructed and some of the quirk inherent in the system.
Colorado State University goes into a bit more detail on how the call numbers are constructed. The first section has information on the classification scheme and the second section describes how to find the book on the shelf.
University of Michigan Libraries Understanding Library of Congress Call Numbers combines the anatomy approach with an explanation of how to read the number. This is a downloadabled .pdf document.
And finally thanks to Lisa The Librarian's blog there is a complete demo tutorial on shelving and reading LC numbers at the LibraryU website. Look for the link "Demo" on the left side of the screen.
Of course you should visit the Library of Congress Classification Outline page where you can download specific sections of the classification system and observe how the system is constructed and spend time exploring Classification Web.