Running programs which do "graphical user interface" operations from home is somewhat difficult, and requires compatible graphics software on your home computer. However, getting a command-line interface on CDF, basically identical to what you get in the "terminal" window in the lab, is relatively straightforward.
There is a remote login protocol called "ssh" which is supported by the CDF computers. That is, the CDF computers run the "server"; what you need for home is the "client" software, which is the other side of a "server-client" connection over the internet. (Similarly, your web browser is a "client" and it connects to a "web server" over the internet.)
Possible client software (all freely distributable) is:
To establish an "ssh" connection to CDF, you need to enter your CDF logname (e.g. c0whatever) and the name of the computer to which you are connecting, for which you can use "cdf.toronto.edu". The first time, it will ask you if you are willing to trust this new computer by saving its public key. After you confirm that, then you will be connected and the CDF computer will demand your password.
When you are connected in this way, as noted above, without extra software you won't be able to run anything "graphical" (i.e. opening its own windows, accepting mouse clicks, etc). You get a terminal window only. But you can do most things in the terminal window.
In particular, you won't be able to run the "nedit" editor over an ssh-only connection (without the X windows software). However, there are a number of editors you can use, which work only within the terminal window, using only text. The one I recommend is "nano", which is the editor portion of the "alpine" e-mail reader you've been using. You can type "nano file" to start editing the file named "file", etc.
Copying files between your home computer and your CDF account is more complicated. I suggest simply working on your CDF account in the first place, whether from home or in the lab. This way your files are always there, all the same, like the advantage of "centralized storage" mechanisms as I'm discussing in lecture. [Yeah yeah yeah, just tell me how to do it anyway]