Simply download and double-click the .msi file to start the Windows installer.
Note that if you already have a previous version of Greenfoot installed, you will need to uninstall it first - go to the Control Panel and then "Programs and Features" to uninstall Greenfoot.
Download the zip file and extract it. You can move the Greenfoot application bundle into your "Application" folder if you wish.
If your version of Mac OS X is too old to run the current version (i.e. pre 10.8.3), go to the 'Old versions' link further down on the downloads page. There you can find previous Greenfoot versions that run on older Mac OS systems.
Download the file and open it to launch the Ubuntu software manager.
Installing Greenfoot this way normally results additionally in the installation of OpenJDK 8. Although Greenfoot may work with OpenJDK 8, it is strongly recommended that you install Oracle's JDK 8 instead. See this launchpad page for details on how to install the Oracle JDK on Ubuntu.
Greenfoot 3 can be used with either OpenJDK or the Oracle JDK. We recommend use of the Oracle JDK for the best experience.
To install Greenfoot using the Oracle JDK, it is necessary to first install the Oracle JDK as a Debian package by creating the package from an Oracle JDK bundle downloaded from the Oracle website. You then use the java-package tool to create a Debian package, which you can install using standard Debian package management utilities. See the instructions for java-package here.
To install Greenfoot using OpenJDK, it may be necessary to add the backports section to your package sources list.
Having performed either of the above steps, install the Greenfoot-linux-351.deb package that you downloaded using the gdebi command:
Download the "Pure Java" Greenfoot installer (which is a '.jar' file). You will need to install a suitable Java JDK separately (since Greenfoot 3.0, Greenfoot requires JDK 8 and uses JavaFX) - it is recommend that you use the Oracle JDK, which you can download from Oracle's "Java for developers" download web page (where you can also find installation instructions).
You may be able to run the Greenfoot installer .jar file by double-clicking it in a file manager; if not, you should open a terminal and enter the command:
java -jar Greenfoot-generic-351.jar
You might need to specify the full path to the 'java' executable (for example, if you have installed the Oracle JDK in '/opt/jdk1.8.0_66', replace 'java' in the above command with '/opt/jdk1.8.0_66/bin/java'). Likewise, you will need to specify the correct path to the installer (i.e. the location that you downloaded it to).
You should then be presented with the installer's user interface, which will guide you through the installation process.