PuTTY is a free ssh client that can be used to connect to our Linux servers. You can read about PuTTY at http://www.chiark.greenend.org.uk/~sgtatham/putty/, or jump directly to the download page (there are many files listed - you only need putty.exe).
Once you've downloaded putty.exe, you are ready to run it. There is no installer, just the single file executable, so it can be placed anywhere you'd like (the desktop is a convenient place for most). Simple double-click on the putty.exe icon to get started.
When you first launch PuTTY, you'll be presented with session configuration options. Here you can can create new sessions and select from existing ones. To create a new session, enter the hostname as indicated, the select SSH for the protocol.
To save this session, next enter a name for it in the Saved Sessions box, then click the adjoining Save button. Your session will now appear in the session list.
Finally, to actually start your session, double-click on the session in the list, or select it and click the Open button at the bottom of the window.
In subsequent uses, you will not have to enter the hostname and select the protocol, only the first time when you create the session.
The first time that you connect to a server, PuTTY will present a warning about the server host key - this is normal behavior. Simply click Yes to accept the key and you won't be presented with the warning when you connect to that server again.
Finally, you will be presented with the actually ssh session window and asked for your login/username and password.
A related HOWTO on using WinSCP to transfer files is also available.