Unless you have a Mac, you will need to install both
    -- the Java JDK (Java Development Kit) (also referred to as SDK), version J2SE 5.0,
    -- and BlueJ .
(On MacOS X, a recent Java JDK is installed by default.)

To install the BlueJ Integrated Development Environment (IDE), go to the BlueJ website:
    http://www.bluej.org/

Here you will find much information, which you can explore later.
To download, use the "download" link in the left column, which takes you to
    http://www.bluej.org/download/download.html

Follow the directions for installation, but you must first install the Java JDK.
When you take the "J2SE 5.0" link (on the righthand side of the BlueJ download page, in the "Systems Requirements" box), you'll get to the Sun downloads page:
    http://java.sun.com/javase/downloads/index_jdk5.jsp

About halfway down the page, you'll want to install "JDK 5.0 Update 10". The download link takes you to a page of choices. Pick the appropriate one for your platform (windows, linux, solaris).

Now back on the BlueJ download page, install the latest offcial release for your platform (Windows, MacOS X, others).