You probably already have icedove installed. Assuming you are using Gnome, from the top menu select:
Applications -> Internet -> Icedove Mail/News
If it's not there, install it with synaptic. From the top menu select:
System -> Administration -> Synaptic Package Manager
You'll be asked to authorize. Enter the password you gave during install for the root account.
In the window that opens, there is a search box in the upper-right corner. If it says "rebuilding search index" then wait a few moments/minutes for it to finish. Then type "icedove" in the search text box. In a moment or two, the section immediately below the search box will update its contents to show all the packages that match. There should be an entry with just plain "icedove" in the first column. Left-click the box next to the name and in the small menu that appears choose "Mark for installation." There should be a button near the top of the window showing a green check-mark labeled "Apply" that is now enabled. Left-click it, and approve the changes in the confirmation window that appears.
The reason it's "icedove" in Debian and not Thunderbird is because the maintainers of Debian did not want to package Thunderbird exactly as it is released. The reason is only because of "branding." That is, some of the artwork and the name itself (I believe) are trademarked or otherwise restricted in their use. The same is true for Firefox. In Debian, the non-branded version of Firefox is Iceweasel. The programs are otherwise identical aside from the images and/or names.
I get an error message saying that my username is not in the sudo directory and that the incident will be reported?? I'm the system admin!
Yeah, Debian does not set up sudo. That's more of an Ubuntu thing.
And setting up sudo is not something I would suggest for a new Linux user like yourself (no offense to you--or EDDY1 for suggesting setting it up). For a new user, the syntax is not intuitive and the man page for the sudoers file will likely be clear as mud.