Booth Library has four Library of Congress Collections: Archives, Juvenile, Reference and the General Collection.
Collection:  Archives  Juvenile Literature (a.k.a. Children's)  Reference  General Collection 
Physical Location:  Closed  Entrance Level  Entrance Level  AK, 3rd floor LZ, 1st floor 
Examples of spine labels for each collection:  ARC PN 4832 .D3 
JUV GV 706.3 .L65 2002 
REF F 106 .E53 2006 

Setting aside the location code (i.e. JUV, REF), a book spine label has at least 3 lines and can have as many as 5 lines.
Line one:
Moving left to right, single letters are filed before double letters. Each letter represents a field of study. For example,
Line two:
The first number on the second line is read numerically, so, the smaller number before the larger number. However some numbers on the second line have a decimal, after the decimal the order is number by number.
e.g.
26.17 BEFORE
26.2
Note that .17 is before .2, because the first number is not seen as seventeen but as two separate numbers 1 and 7, review one number at a time until there is a difference.
Here is what these numbers look like in order, on the shelf, reading left to right:
Line three:
The letter is organized alphabetically, the numbers are filled BY NUMBER not numerically, so, .E359 before .E39.
Think of it this way, .E359 before .E39 because the number is not three hundred fifty nine, there are three seperate numbers: 3 and 5 and 9, review one number at a time until there is a difference. Here's the illustration:
Line four:
Occasionally there is a fourth line. It is organized the same as Line Three.
Here is what the books would look like in order, on the shelf, reading left to right:
The final lines on the spine label could be the year and/or a volume.