A very good Debian reference is, well, the Debian Reference Manual. However, it's rather lengthy, so here's a quick introduction to some of the keys differences, as compared with other distros.
In Debian, when you use su to get root privileges, the X authority is not transferred to root, so you can't start X programs. There may be a security-related reason for this, but I don't know what it is. If you need to run an X program, you must first do for example
xauth merge /home/nodwell/.Xauthority
This might leave the .Xauthority file owned by root, so you may have to transfer ownership back again if you want to run any X programs as the original user.
chown nodwell /home/nodwell/.Xauthority
This obviously won't work for NFS mounted home directories with root squashing. An alternative is to ssh as root to localhost, which works when ssh is configured to accept logins from root, and to enable X forwarding.
dpkg is the Debian equivalent of rpm. You rarely need it, because you almost always use apt instead. But if you get a .deb file from somewhere, it can be useful.
apt-get update makes apt download the current list of packages from the servers. apt-get upgrade will install any available newer versions (after asking). Since we're running the testing branch, there will be some new packages every week. This might be a nuisance, or not, we'll see. Sometimes on upgrading, apt will tell you about packages it won't upgrade. There can be several reasons for this. The most common is that the newer version of the package to be upgraded has a new dependency, some other package which is not installed yet. Upgrading won't install new packages. You can make apt upgrade the package by telling it to install it. For example, if it tells you that it won't upgrade foo, then running apt-get install foo will force it to upgrade.
If you're looking for a particular package, you can search the packages names and the short packages descriptions with apt-cache search, for example
apt-cache search emacs
You can read the complete description of the package, along with dependencies and suggested packages, with
apt-cache show epiphany-browser
An alternative to these commands is the Debian Packages web site, which allows the same sort of searches, as well as searching by file name, and browsing by category.
I really recommend that when installing packages, you check out the descriptions either on the web page or with apt-cache show. apt only automatically installs the required dependencies, however the recommended and suggested packages are very often also useful, and you won't know about them unless you check.
You've probably noticed that some packages require input for configuration at the time that you install them. If you want to change the configuration later, run dpkg-reconfigure. For example
dpkg-reconfigure ntp-simple
will allow you to select different ntp servers. Of course, you could modify the relevant configuration files directly, but dpkg often provides a much simpler way.
It may happen that for some reason you want to recompile a debian package with slightly different flags, or perhaps you want to backport a package from unstable (probably not if you're running testing, but on a "stable" system, this is sometimes useful). This is surprisingly easy to do. Instructions for doing this are here. To modify the compile flags, edit the debian/rules file.
If you install multiple programs which can perform the same function, you can choose which will be the default with update-alternative. Look in /etc/alternatives for all the possible alternatives which you can set. For example, if I want to set the default browser, I can run
update-alternatives --config www-browser
which will present me with a list of choices.
Generally the environment variable MANPATH should not be set, since it overrides the system defaults, which are in /etc/manpath.conf. Debian packages automatically update this file, but if you install some proprietary software, you can manually edit this file to add additional paths to man pages.