You need Java 1.5 (or higher) to run jMemorize. To start the application just (double-)click the icon or type in javaw -jar jMemorize-[version].jar from command line.
You can find the current changelog here. The most current builds are.
Windows users can use the simpler installer version.
As this software is released under the GPL license you can also get the zipped source code packages. You can even access the repository directly. See the development page for more informations on how to do this.
For older versions please check the SourceForge release archives.