Got audio working in Debian. It was a simple process, really.
Googling threw up a command to configure Audio. alsaconf .
ALSA is an acronym for Advanced Linux Sound Architecture. Simply put, audio drivers for Linux, something that helps to generate noise out of the speakers. Without these in place, the speakers wont even generate noise.
Installation of Alsa was pretty simple. Open up a root shell, and issued the command
apt-get install alsaconf
The name of the correct package was alsa-utils, not alsaconf as I had typed in. Apt figured this out automatically, downloaded and installed the packages alsa-base, alsa-utils and lsof.
After these packages were installed, I ran alsaconf from the root shell. My sound card was detected and configured properly. Adjusted the volume using Kmixer, and voila, my speakers came to life 
.
Enjoying Spirited Away right now. A masterpiece by Hayao Miyazaki.
