Well, while waiting for my soon-to-be tutorial, I can give you just some 'directions' ;-)
You need PuTTY - get it here.
Launch it, use data provided by your hosting to connect via SSH:
Enter the host name (or IP address), OPEN session, you'll see a black screen, then type your username to connect to your account, then type password. That's it:)
Now type 'cd' to see list of directories. Type 'cd name-of-dir' to enter a certain dir. Type 'cd ..' to go level up. Type just 'cd' to go to the root of your account:)
Only other two commands I use are 'cp' and 'rm' to backup and delete files for my WP upgrades.
There are lots of tutorials on how to use SSH in Unix, though. Just search! :)
There is also very good documentation at wordpress.org, as to how you could perform upgrade using SSH. Check it out!
Be careful, you can delete everything in a second on your server account using "rm -rf", so practice first (in a test dir on the server for example) and learn basic syntax of SSH commands - copy, delete, move from dir to dir, etc. :)
PS There's also Midnight Commander, you can launch it by typing 'mc', it's like Norton Commander in DOS, via MC you do everything and you do not need to know the commands by memory ;-)