First of all, I would like to state that the chance you'll get a failure is very small. However, knowing the procedures for distress and urgency situations are good to know.
The following procedures reflect real-world procedures:
Distress messages
A distress message should be issued when you are in a situation of huge danger and/or upcomming danger which requires immediate assistance from ATC.
A distress call should be made on the frequency you are currently on, if nobody responses, make the call again on 121,5.
When you are in distress, your concentration is focussed on the aircraft. However, try to make your distress call as complete as possible.
1) Mayday, Mayday, Mayday
2) Station you are currently on (e.g. Schiphol Approach)
3) Your callsign (e.g. EHM1234)
4) the emergency (engine 2 failure) (engine numbers are counted from left to right, so the outer right engine of a 747 is engine 4)
5) Intentions of the captain
6) Position, altitude and course of the aircraft
7) Other useful information
When you are in distress, set your transponder code to 7700. If you are hijacked, set your transponder code to 7500. If a hijack gets out of hand and you're in emergency, set it to 7700.
Urgency messages
An urgency message should be issued when not immediate assistance is required. This can be related to your own aircraft or to something else. For example: If you see a small aircraft crashing in the fields then you should issue a urgency call too.
An urgency message should be made at the current frequency first, when you get no response: make the same call again at 121,5.
An urgency call looks like this:
1) PAN PAN, PAN PAN, PAN PAN
2) Call sign of the ground station (e.g. Schiphol Approach)
3) Your callsign (e.g. EHM1234)
4) Description of the urgency situation
5) Intentions of the captain
6) Position, altitude and course of the aircraft
7) Other relevant information
