First, do you have Java installed? You need Java SE 1.6 or 1.7 to play Salem. You can download and install it from
http://www.java.com/en/.
When you have Java installed (or if you already do), the file you downloaded is the launcher. Just open it like you would any other application. There will be a download and processing which can take a while on some systems. After that is done, the game will open.