It's tougher to give an installation guide for Linux because of the large variety of different distributions and architectures. Here is a rough guide that will work for many distributions such as Ubuntu.
1) Install Java Development Kit (JDK)
Follow the above link and click the "Download" button next to the "JDK 5.0 Update 9". (NOT the "with NetBeans 5.0" link or the "with Java EE" link or others). Accept the License Agreement and choose the "Linux self-extracting file" file:
(If you use a Linux distribution that supports RPM packages such as Fedora Core, you may wish to use the "Linux RPM in self-extracting file" package.)
Once you have finished downloading the JDK .bin file, open a terminal window and execute the file. You may have to give execution permissions to the file:
chmod +x jdk-6-linux-i586.bin
Running the .bin file extracts the JDK contents. Move these to a directory of your choice. (The rest of this tutorial assumes you have moved the JDK to /usr/lib/jdk/ .)
After installing Java, you will probably wish to add Java's directory to your PATH setting, so that you can run Java commands from your terminal. To do so, edit the file .bashrc in your home directory and add the following lines to the end of it:
You should close your terminal and open a new one for the PATH changes to take effect.
2) Download DrJava editor
Find the section labeled "Current Stable Release," then click the button labeled "Download Jar File." Choose a download mirror and save the file named drjava-stable-20061025-1556.jar to a convenient location.
Once the file is downloaded, open a terminal window, change directory to the one that contains the DrJava Jar file, and type the following:
java -jar drjava-stable-20061025-1556.jar