The JCTerm applet should start automatically. (The first time it tries to run, you may be asked to give it permission.)
Once it starts, go to File and choose Open SHELL Session. When it asks for username@hostname, you would put, e.g., yourusername@puma.math.arizona.edu.
If the applet won't start, or if you prefer running JCTerm in its own window—independently of the web browser—then launch JCTerm as an application (requires JavaWebStart). Once it launches, go to the File menu and choose Open SHELL Session.
JCTerm 0.0.9 from JCraft, licensed under GNU LGPL.