HSQLDB is a small database manager written in Java. It can be used in several modes, basically Server mode and In Process (embedded within your application) mode. But all this can be found on http://hsqldb.org/web/hsqlDocsFrame.html.
90% of the documentation I have found for developing with HSQLDB is related to using an ide such as Eclipse, or IntelliJ.
If you want to dispense with those tools you can do so by following these instructions:
download hsqldb from http://sourceforge.net/project/showfiles.php?group_id=23316
unzip that file, inside of which you will find a lib directory and inside of that lib directory you will find HSQLDB.jar.
In the directory you are building your application unzip the HSQLDB.jar which will create a META-INF directory and a org directory
The next step is a bit of coding for your application. I have explicitly caught all the relevant exceptions in this code, but they can all be replaced with catch (Exception e)
/* Register the hsqldb driver to JDBC */
/* Create a connection to the testdb, located in the same working directory as this code */
Connection c = DriverManager?.getConnection("jdbc:hsqldb:file:testdb", "sa", "");
/* Handle all the exceptions */