There should be a shaft for both ***** to be pushed onto. If it's not there there's no doubt that it broke off and is probably attached to the old **** you may have thrown away. In any case once the shaft is broken the fan switch is useless. Go to the dealer and purchase a new fan switch.
To put it in you need to remove your stereo, center console/cupholder, cig. lighter & ashtray and the dash bezel. Removing the bezel requires you to pop out (carefully, the plastic is easily damaged) all the vents and switches to access hidden screws. Once that is off you have access to the climate control screws. from there it's pretty much self-explanitory. Screw the new switch on, plug it in, and throw it all back together.
Hope this helped