I would like to know how to install .deb packages without using a package manager such as dpkg. Is it possible to do this? What files do I have to edit? Or is there a unique procedure for each package?
You can unpack a .deb package using
Every .deb package contains the two files
Quite likely this scripts don't work on a Non-Debian system but they may contain code you need to run to make the program work.
Why do you want to do this?
Why do you need to do this?
The .deb file contains files to be unpacked in specific locations in the filesystem, including configuration files, and some scripts to be executed before and after installation, upgrading and removal of the package. Failure to run the appropriate steps will result in a borked installation, which will be really hard to revert if the files are not under package manager control. Also, running the scripts may require some environment that's set up by the package manager and that may be quite difficult to replicate by hand.
That said, you can unpack a .deb file by hand:
this will leave three files: control.tar.gz, data.tar.gz and debian-binary. The two tarballs contain the control files, checksums and scripts (control.tar.gz) and the actual files to be unpacked on the filesystem (data.tar.gz). You may be able to get what you need by unpacking and analyzing these files.
Read more about the .deb package format here: http://en.wikipedia.org/wiki/Deb_%28file_format%29
But to stress the point again, this is not really recommended and you stand a high chance of ending up with a borked install.