This page allows you to download several different version of Java. You need to download the version called "JDK 5.0 Update 11". Accept the license agreement and click the "Windows Offline Installation, Multi-language" link to start the download. Once the file finishes downloading, install the JDK. The installation is straightforward.
Next, you need to download BlueJ. You can download it from this page: http://www.bluej.org/download/download.html
Click the link called "bluejsetup-213.exe" to download the installer. Once it's finished, install BlueJ. Again, the installation is pretty straightforward.
Start BlueJ after it is installed. In most cases, it will simply start and work as expected (BlueJ usually can automatically detect the correct JDK). If this is the case, you can now begin using BlueJ. However, BlueJ may prompt you to select a JDK. If this happens, please select the 1.5.0 version of the JDK that you just installed.
If it does not appear that a JDK is available on your system, please click the Advanced button and then the Search Drives for All Java Versions button. The recently installed JDK 1.5.0 should be listed. Select it and continue. After this, BlueJ should work properly.
Instructions compiled by Brian Carter.