Ideally Mayday and Pan calls are made and all traffic conducted on 121.5 MHz, the international aviation distress frequency. However, if an aircraft is already in contact with a ground station an emergency can be declared directly to the station the aircraft is in contact with if that is easier for the crew. It is then the responsibility of the ground station to advise other aircraft of the emergency and request they change to another frequency or cease transmissions for the duration of the event.
Mayday and Pan calls should strictly speaking only be made on the international distress frequency 121.5 and are intended as an open transmission requesting assistance from all and any stations receiving the broadcast.
This doesn't apply if you are already talking to ATC or the control tower somewhere, so simply stating that you are declaring an emergency is usually sufficient (even in the local language if that makes communications clearer). Sometimes you will be asked if you are declaring a Pan or a Mayday which are trigger words allowing an airport controller to determine and activate the appropriate level of emergency response.
Basically in a real emergency you are permitted to communicate by whatever means possible, on whatever frequency you can, so long as the nature of the emergency and the intentions of the aircraft commander are made clear to those on the ground.
Learned all this over 40 years ago when aircraft still carried radio officers. Aircraft today are much more likely to declare an emergency on whatever frequency the radio happens to be tuned to at the time, especially if the pilot(s) are busy trying to sort problems out.