Before answering 500 mans question I think I need to put a bit of context to my answer. What I am talking about is what I teach for the PPL student or low time PPL pilot. Since this group by definition does not have the benefit of a lot of experience a framework of procedures IMO is of significant practical value in helping them deal with abnormal situations.
So first we have to talk about the most likely scenario that a PPL will experience. It is not a sudden total engine failure with no warning, it will most likely be engine roughness and/or a reduction in engine power. The engine will still be running and producing enough power for the aircraft to maintain altitude, but the pilot feels that there is something definitely wrong.
The school I teach part time at flies C 172P's and for this scenario I expect them to go to the emergency checklist where I have added a checklist for engine roughness/Reduction in engine power. I want the student to methodically work through the checklist so that they don't forget anything.
It goes like this
Engine Roughness/Reduction in Engine Power
-Carb heat.........................................Full On for at least 30 sec
-Primer..............................................Full in and locked
-Engine gauges...................................Check
Note 1: if severe carb ice exists engine will initially run very rough until ice has cleared)
Note 2: If high oil temperature or low oil pressure is noted go to that checklist
If problem persists
-Carb heat........................................Cold
-Mixture ...........................................Full rich then lean to max RPM
If problem persists
- Mags............................................Select right and left mag individually
(Note if engine roughness is more pronounced on one mag select the other mag or both, whichever gives smoothest operation)
----------------Land at nearest suitable airport------------------------
If problem persists
- Fuel selector.................................Left for 2 mins
If problem persists............................Right for 2 mins
---------------Land at nearest suitable airport-------------------------
In addition to to this I have emphasized the importance monitoring the engine instruments in flight. Instructors now periodically and without warning cover the oil temp/press gauges and make sure the students know where the needle is actually pointing. (In the green is not a good enough answer ).
With respect to abnormal oil press/temp indications, these can indicate an developing mechanical internal engine failure potentially resulting in a total engine failure. This is the least likely cause of an engine failure but they do happen. The good news is there will almost always be some warning. Any internal misalignment or failure will almost always result in metal rubbing. This will cause a rapid rise in oil temperature with the oil temp gauge pegging at its maximum value. A dramatic drop in oil pressure will quickly follow. Any engine showing these signs should be presumed to be in danger of imminent total failure and appropriate actions to land ASAP should be taken. The only caveat is an open circuit in the oil temp wiring will cause the oil temp needle to peg at the highest temp. However in this case the oil pressure will be normal so it is likely just the gauge. However a landing at the nearest suitable airport would be prudent.
The next level of checks (Again for a C 172P) is a memory "cause check" intended to restore power when the engine fails or is producing so little power that the aircraft will not maintain altitude and
with the aircraft more than 1000 feet AGL. If the aircraft is below 1000 feet then no cause check is done and the pilot concentrates on flying the aircraft to a survivable touch down point.
After establishing the gliding attitude and pointing the aircraft at the nearest survivable forced landing area.
Carb heat.......Full on
fuel ..............Both tanks
Mixture .........Full Rich
Mags.............Both/left/right/both
This check can be done in about 5 seconds if practiced. By that I mean every couple of flights you make a point of going through the sequence touching each control to build muscle memory.
If the reason the engine failed was caused by a mistake you made ( eg missing a build up of carb ice, running a tank dry, forgetting to enrichen the mixture and then adding a bunch of throttle) then these simple actions will restore power and instead of potentially wrecking a perfectly serviceable airplane after you smashed it into a field when the engine stopped, you will restore power, and fly away vowing never to do that again.
Don't forget that the accident statistic show that up to 80 % of the engine failures are caused by the actions or in actions of the pilot. The Cause check won't save you if you have run out of gas but it will save you from some other mistakes that are not all that hard to make.
Finally I also discuss the high altitude engine failure. This is one where you are cruising along more then 5000 feet above ground and you suffer a failure or gross loss of engine power. After doing the cause check and all the other appropriate actions preparing for the forced landing, assuming you are well placed for the field it may be possible to do some more advanced troubleshooting. A variety of carburetor/fuel injection failures can result in the engine only running at certain throttle or mixture settings. So consider going to mid range throttle setting and starting from full rich and then slowly leaning towards ICO. If that doesn't work go back to full rich and starting from full throttle slowly retard the throttle. Is that doesn't work try giving the engine a shot of prime. If the engine starts and then dies you can get some power back by setting a low throttle setting and continually pumping the primer. The little bit of power you can get may provide a useful stretch to the glide. However I must emphasize that these techniques
must not get in the way of flying the aircraft and should be instantly abandoned if you start feeling pressured by trying to trouble shoot and manage the forced approach.
Finally I have presented the checks meant for a C 172P. They apply to most light GA aircraft except for C 172R or S models or other aircraft with fuel injected engines so for these aircraft where the check says carb heat insert "alternate air" and for low wing aircraft like Pipers and Grummans where the check says fuel to both, insert fuel.... change tank and boost pump on.
So 500 man, I Hope that answers your question.