First of all, you need Java 1.5 JRE. You can download it here.
Pretty easy. Open a new terminal (for windows users, go to Start Menu > Run and type "cmd.exe"). Type java -version. If Java 1.5 is installed, you should see java version "1.5.0".
Just download BakuBakuAnimals.jar. To execute it, just double-clic on it (for windows users only). If you're not on a windows OS (or a bit pervert), open a terminal and type java -jar BakuBakuAnimals.jar. If you have troubles doing this, just send me a mail.
And you have good ears. Here it is : a clone of Puzzle Bubble, called Hubble Bubble. There is a windows version, a flash version (swf file). Moreover, for multiplayer game, there are a windows server and a unix server avaible. And of course, a manual.