I recommend reading the detailed installation steps which are provided here: http://thegoan.com/firebible#installation
A brief overview of these steps is presented below:
On Windows and Linux, FireBible requires the Oracle JRE to function, on the Mac, the Apple JRE is sufficient. JRE 5 and above is preferred.
Test your JRE here: http://www.java.com/en/download/help/testvm.xml
Download an Oracle JRE for Windows / Linux here: http://java.sun.com/javase/downloads
If you are using a Java 7 JRE, you will need to update it to be at least Java 7 update 7 or higher, prior versions are disabled in Firefox due to security vulnerabilities.
FireBible uses JSword to read the Sword modules, JSword is a Java based library which can be downloaded here: http://crosswire.org/jsword/download.jsp
Once downloaded and unzipped, add JSword to FireBible by going to Tools > FireBible > JSword and select the JSword folder.
Videos demonstrating FireBible can be found here: http://thegoan.com/firebible/screencasts