If you look under the Firefox "Tools" menu you should see a Toodledo submenu. On that menu there is a "Settings..." option. That will bring up a dialog box where you can input your username and password.
I get exactly the same behaviour as len250 had, even though I set the email adress and password in the settings box to exactly those I use to login to the site from the browser (ie not the tool) successfully. Password and email are shown correctly (and identically) as properties of the chrome://toodledo and http://www.toodledo.com URLs in the firefox password manager.
The password has punctuation in it. Could this be related to an earlier bug with \ appearing in passwords?