All you need to do is lift up your index finger off the left side of the mighty mouse, and then click the right side of the mouse using any of your free fingers. The mighty mouse does not register the right click if your finger is resting on the left side of the mouse.
You have to enable right-click ability in system preferences (through the Apple icon menu on the top menu bar.) You can also press ctrl button and click the single mouse button to get the same effect.