There are a few ways to install a copy of JUCE:
git clone --depth 1 git://juce.git.sourceforge.net/gitroot/juce/juceThe JUCE source code all lives in a folder called, unsurprisingly, juce, which you can unzip
and put somewhere on your system.
The latest GIT change-log can be viewed on SourceForge here
To browse the JUCE source tree on SourceForge, click here
A complete doxygen-generated API reference guide is available for browsing here.
The Juce source tree includes a simple application (in juce/extras/JuceDemo) that shows off a few of
its features. Some pre-compiled binaries of this demo app are available from the SourceForge downloads page.
As well as the demo, there are a bunch of projects in juce/extras that provide good examples of how to use the library classes.