The Deluge daemon installs and runs as a specific user (named "deluge" on Debian). It sounds like you have a daemon not running as the system daemon and/or pointing at a different home/configuration subdirectory.
For me the key was to ensure that this user's home directory is created and that Debian recognizes this user's home subdir as the user's home. This is important because since the daemon will be running as the deluge user, the daemon will then create a subdirectory tree of ~/.config/deluge/* which will contain the various config files you'll need to edit.
With Debian Wheezy (the current stable version of Debian),
the site's install instructions work fine. But before I installed those package(s), I created a Debian user named "deluge" as per the instructions
here or
here. I changed that adduser statement a bit to point to a subdirectory named /opt/torrents as deluge's home directory, but that is purely a cosmetic choice.
Okay, let me summarize the above chaotic mess, this is what I did:
1) Uninstall all deluge packages to start from a clean/blank slate.
2) Create a user named deluge and give that user a home directory. Change the ownership of deluge's home directory to make sure deluge can read/write to the directory.
3) Install deluge -- at least the daemon and the web portions. (The command-line client is also handy and pretty slick.)
4) Create a daemon script for /etc/init.d to run the daemon on boot (explained in the two "here" links above).
5) Run the daemon once to create default config files in ~/.config/deluge/*
6) Stop the daemon and make sure it's not running (it'll overwrite its config files on exit).
7) Edit the config files to your liking and then restart the daemon.
At that point you should be able to log in with the web client pointing it to localhost, or log in remotely with a GUI client if your configuration allows remote connections.