SFTP is a good way to transfer files across untrusted networks.
You will need a client:
Systems running SFTP
Open the program, you should get a display like this:
Enter the address you'd like to connect to and your username/password. Click connect, if you've not connected before you will see something like:
If the line beginning ssh-rsa is identical to the fingerprint in the table above, you are connecting to the correct server and can click yes. Otherwise, you're probably connecting to a different server. Once you're connected you will probably get a window divided into two parts:
You can drag and drop between these two panes, which should bring up a dialogue like this:
Most of the time just click "Copy"
I can now drag and drop files.