Most TETRA radios have an emergency button, too. It can be programmed to make a call to the selected group or a predefined number (individual, group or external), or send an ident and the system will route the call based on the emergency target number defined for each radio subscriber (again individual, group or external). If the target is not reachable the call is routed to an alternative number.
Accidental activation can be prevented by setting a timer, e.g. the button must be pressed for, say, 2 seconds, else nothing happens. Programming the radio is a matter of minutes, but requires special software and perhaps a hardlock/dongle from the vendor (for obvious reasons).
The most important aspect is however that the call is treated as an emergency call in TETRA networks, i.e. it knocks out another, normal priority call if there are no free resources in the system. It's also possible that the microphone is activated automatically ("hot-mic") so that the user in distress does not need to press PTT to talk and radios with GPS may send the position information automatically.
Note: Some of the functions described above are system and/or vendor dependent.