Can I transfer files using SSH?

Use the PSCP tool from the putty download page:

http://www.chiark.greenend.org.uk/~sgtatham/putty/download.html

PSCP is the putty version of scp which is a cp (copy) over ssh command.

PSCP needs to be installed on your windows computer (just downloaded, really, there is no install process. In the Packaged Files section, pscp.exe is already included). Nothing needs to be installed on the school's servers. PSCP and scp both use ssh to connect.

To answer the usage question from the comments:

To upload from your computer to a remote server:

c:\pscp c:\some\path\to\a\file.txt user@remote:\home\user\some\path

This will upload the file file.txt to the specified directory on the server. If the final part of the destination path is NOT a directory, it will be the new file name. You could also do this to upload the file with a different name:

c:\pscp c:\some\path\to\a\file.txt user@remote:\home\user\some\path\newname.txt

To download a file from a remote server to your computer:

c:\pscp user@remote:\home\user\some\file.txt c:\some\path\to\a\

or

c:\pscp user@remote:\home\user\some\file.txt c:\some\path\to\a\newfile.txt

or

c:\pscp user@remote:\home\user\some\file.txt .

With a lone dot at the end there. This will download the specified file to the current directory.

Since the comment is too far down, I should also point out here that WinSCP exists providing a GUI for all this, if that's of interest: http://winscp.net/eng/download.php

You might have to use forward slashes (/) to talk with LINUX/UNIX servers

c:\pscp c:\some\path\to\a\file.txt user@remote:/home/user/some/path

You can use WinSCP for this. It's much easier than the other tools listed, it provides a simple drag and drop UI.