To install JSoko you just need to unzip the file you have downloaded.
You can use any program that can unzip compressed files (for instance the program http://www.7-zip.org).
Of course you must have the permission to write to the folder you want to unzip the file to.
That's all that has to be done.
For instance, when you have downloaded the file JSoko.zip you can unzip it to the folder:
The program doesn't stores files outside the folder you have unzipped it to. This means you can just copy the folder "JSoko" to any other storage (for instance an USB flash drive) and then play from there.
Note: the program also saves the user settings into the folder it has been installed to. The program doesn't use a private settings file for each user of the program. Hence, all users share the same settings file. If a specific user wants to use different settings than another user it's recommended to copy the whole JSoko folder to another folder.
In order to use the program the Java runtime environment (http://java.com) has to be installed. JSoko needs the Java runtime environment (JRE) 6 or higher.