No installation is required for MagicTree. The application is distrubuted as a single JAR file which has to be executed with JRE. Just save the file on your desktop. Double-click on it to execute it or, for less user-friendly OSes, issue "java -jar MagicTree.jar' command.
On startup, it will automatically create .magictree directory under users home directory (C:\Documents and Settings\USERNAME\.magictree\ on Windows) and unpack necessary files there. The files will be overwritten if JAR contains more recently modified files. Thanks to this files changed in the most recent build will replace old ones, assuming your local clock is correct.
Beta version of MagicTree writes a lot of debugging information into magictree.log file, located in the directory the JAR file is executed from.
A default installation of Ubuntu does not contain Java JRE. Unless you have a reason to do otherwise, install openjdk's JRE. The following command can be used on Ubuntu 10: "sudo apt-get install openjdk-6-jre". See https://help.ubuntu.com/community/JavaInstallation and https://help.ubuntu.com/community/Java for more information about Java on Ubuntu.