Decompiling Maps
Decompiling is the process of taking a compiled level and generating a source that can be opened in a map editor. Decompiled levels mimick the original source, they are not exact reproductions. This makes them useful for learning, measurement, and inspection, but not direct recompilation. The original source is ideal for reproductions or modifications.
Releasing reproductions, modifications, or approximations of another's work without permission is breaking copyright law.
Tools
Getting dirty
To start off, you are required to have installed the Java Runtime Environment (JRE), which can be downloaded from http://java.sun.com/javase/downloads/. It allows your computer to run Java applications. Once installed, you are ready to decompile your first map. Download VMEX and copy it to the Source SDK bin folder. You'll notice VMEX comes with two .bat files which can be run to start up VMEX.
To decompile a map run VMEX and browse to the map, then hit decompile.

See Also
Before you go
Before you take this jump to run off and decompile a map take a second or two to think, "What am I trying to learn/do?". Read the included TXT files, you may just find the creator's e-mail, and that could be more helpful than you imagine.
Some mappers will offer up help and advice, they may even go so far as to provide perfect examples of what you were trying to "borrow" from the map.