The Windows releases of the application come with their own JRE 1.7, so you do not need to have Java installed. For Linux or in case you have simply downloaded a jar file, you will need at least Java 7 in order to run the application.
In terms of hardware requirements...
You can start the application either by double clicking the rootgui.exe executable file, or (if you have Java 7 installed) through the command line, as shown below.
Using the jar file you downloaded, simply execute it as any other Java jar file:
java -jar rootgui.jar