First of all, you shouldn't be worrying about to which directory JRE is going to be
installed, this is something that a package manager tool (like apt-get) will take care of.
To install Java and verify results, follow these steps:
a) Open terminal
b) Use apt-get to install required packages by typing:
sudo apt-get install sun-java6-jre sun-java6-plugin sun-java6-fonts
c) To verify that Java has really installed, try typing:
java -version
d) If this is OK, then try testing if the Firefox plugin is installed and running, by typing the following URL to the address bar:
about:plugins
You should find references to Java there.
When you've figure out which step did not work, it is much easier to troubleshoot!