OK, easy enough.
SSH tunnelling works like this: the SSH client opens a port on the client machine, and connects that through the SSH tunnel to a machine accessible by the server.
Then, a program running on the client side can connect to the open port, and it will behave as if it is connected to the machine on the server side:
program -> client: port -> (SSH tunnel) -> SSH server -> target: port
You can also set up a SSH tunnel in the opposite direction (for running a server on the SSH client machine) but that's used less often.
Instructions: in the Putty options box, set up a port forwarding, connect local port 6667 to 'localhost:6667' on the server side (I'm assuming your SSH server is also your IRC proxy server!)
Then connect your IRC client to 'localhost:6667' and it will get forwarded to 'localhost:6667' on the server, i.e. the IRC proxy server.
Oh, and don't do this if it would constitute an illegal act or a breach of service contract, explicit or implied. If it could get misconstrued as such an act, don't get caught.