Q: Where is the Other Options button described in the instructions for airport utility 6 above?

If you are using an AirPort Express with a 3rd party wireless router, the "Join a wireless network" option should automatically appear when you start up the setup "wizard".  In the example below, the Express will be setup to join a Uverse wireless network.

Although "Client Mode" is never mentioned anywhere in AirPort Utility 6.x, or 5.x for that matter, when the Express is set up to "join" a network, it is in fact in client mode.  Apple does not exactly make this very clear.

You should not need it, but the Other Options button is located down at the lower left of the window in the example above. Choose the "Add to an existing network" option if the setup screen does not first suggest that the Express will be set up to "join" the network.

If you are using an AirPort Express with another Apple router, the setup wizard will automatically configure the Express to "Extend a wireless network". Once that setup is complete, you can go back in using AirPort Utility and manually change the setting for the Express from "Extend a wireless network" to "Join a wireless network" and then Update to save the new settings.