1. Save the Azureus file somewhere, For Examnple: /home/you/bin
2. Open a terminal (xterm, bash, aterm--whatever you have) and type cd /home/you/bin (or just cd bin since the terminal should default to your home directory when you open it).
3. In the terminal type tar- xvjf filename.tar.bz2 (replace 'filename' with the actual filename of course).
4. Type ls (this will show you files and folders in that directory, there should be a new one called Azureus, or something similar. Let's pretent it is called Azureus.
5. Type cd Azureus (cd is change directory, so now you are in the /home/you/bin/Azureus directory)
6. Type ./azureus and follow the instructions.
Not working? Read the README file, or the INSTALL file.
You'll need the java runtime libraries for Azureus to work.
You really should read up on using the Terminal, for your success on Linux depends on it.