I found this article to be fairly helpful when it came to installing Sun's JRE under Debian Linux.
However, there was one step that I needed to add that was missing:
apt-get remove java-gcj-compat
Without that step, the GCJ Java compatibility scripts remained, conflicting with Sun's Java. Since that package was installed by default with my Debian Testing install, I expect other people will run into the same problem.
The basic steps are:
sudo apt-get install java-package
fakeroot make-jpkg <java-binary-package-name>.bin
sudo dpkg -i <created-package-name>.deb
Note that you can obviously run the "sudo" steps directly as root from a root shell, but the fakeroot command must be done as a non-root user. (Since "fakeroot" will have no effect if you're root...)