Windows -
(These directions are specific to Windows XP, though they should hold for Vista as well)

On Windows you will need the Java Development Kit to run Dr Java. If you already have the JDK skip down to installing Dr Java. (Note: Java 6 is known to cause problems with DrJava. Please contact Isaac (overcast at evergreen dot edu) if you need help with this).
1) Go to the Java Downloads Page [1].
2) Choose the "Download" button in the box labeled "JDK 5.0 Update 14".
3) Check the box to indicate your agreement to the license.
4) Click on the link for the "Windows Online Installation".
5) Once this file is downloaded, locate it and double-click on it.
6) Walkthrough of the JDK Installer:

a) Choose "accept" on the License Agreement page.
b) If you care to save yourself the download time you can safely disable "Source Code" and "Demos" otherwise just click "Next".
c) The installer will download ~100MB, so be patient.
d) More "Custom Setup" follows this. It's best to just click "Next".
e) Choose "Finish" and then you're done

To Install Dr Java:
1) Go to the homepage [2].
2) Choose "Download Windows App".
3) Once the download succeeds you should be able to double-click on the DrJava icon to start it up.

Mac OS -

1) Go to the DrJava Home Page [3]
2) Click on the button labeled "Download Mac OS X App"
3) This will download a file in tar.gz format.
4) Once the download is complete, double click on it to extract Dr Java.
5) You are now ready to go!