If you use the wireless programming kit, then you should connect it correctly then go to Robot >> Advanced Tools >> VEXNet Joystick Viewer on your RobotC software. This has a built-in competition switch
Adding on, there is no current way (to my knowledge) to trigger autonomous when you push a button if it is in the autonomous task. However, if you want to test your auton, you could just put an if statement that activates your auton when a button is pushed in user control. It should (theoretically) work.
You could also set a boolean flag to true, start the autonomous task from driver control which would know to know to kill the user control task when auto starts and start usercontrol when auto ends based on this flag.