Just open the downloaded alloy4.dmg file (available at alloy.mit.edu), and double click on the Alloy4 icon. To keep the application, drag the icon out of the dmg window and place it somewhere in your home directory or on your desktop.
Running the Alloy Analyzer on other platforms
Just download the alloy4.jar file (available at alloy.mit.edu) then double-click on the jar file, or type:
java -jar alloy4.jar
in the console.
Please note: Platform-dependent libraries are currently available only for Mac OS X, Windows (x86), Linux (x86), and FreeBSD (x86). On other platforms, you can still run the Alloy Analyzer, but you will need to select the pure Java solver “SAT4J” (through the Options menu).