Good timing -- I'm going to recurrent training next week. The following is specific to MD90s, but generally is very similar for most airliners and airlines.
>from the moment you notice there is a problem
>with one of the engines...
You'll notice it in any number of ways you can imagine. If you're real good you'll probably see a very slight oil pressure fluctuation or slow decrease as a first sign of possible problem; but realistically, think more in terms of a caution light and/or aural warning (bell, horn or whatever the particular aircraft uses).
Procedurally, there really is no procedure at this point as there are too many variables. Ultimately the captain will either decide to shutdown the engine as a precaution, continue operating the engine with caution, or the situation may deteriorate to the point that procedurally the crew is required to shutdown the engine.
>...to the moment you shut it off...
AA utilizes two basic scenarios that are basically (a) Major Damage/Fire and (b) no major damage/no fire.
(a) Engine Failure/Inflight Engine Shutdown.
-- Throttle (affected engine)........ IDLE
-- Fuel Switch (affected engine)....OFF
(the engine is now effectively off and windmilling)
-- Pneu X-Feed Valve (affected engine).....CLOSE
(isolates bleed air systems)
-- Fuel PUMPS Switches and Fuel X-Feed Lever....AS REQUIRED.
(turn of unused pumps and permit use of all fuel to remaining engine)
-- Electrical Loads.........................CHECK
(not required--turn on APU to reduce load on remaining generator)
-- AIR COND SHUTOFF Switch..........OVRD
(re-establish air conditioning and pressurization)
-- AIR COND SUPPLY Switch (affected engine).....OFF
(closes valve to a/c pack)
If you suspect Fire/Severe Damage, insert the following after Fuel Switch...OFF:
ENG FIRE Handle (affected engine).... PULL
AGENT DISCH...............................1 or 2
That's the basic procedures, now all you've got to do is apply them to the multitude of different situations you can think of, modifing appropriately for each situation.
>...and then how do you cruise ...
On one engine.
>...how do you land the plane with one engine
>flaps settings setting speeds etc etc....
"Use Normal Approach Procedures."
"Use Flaps 28 for landing."
"Use Flaps 11 for go-around."
Caution using reverse thrust with only one engine.
With the above noted exceptions, everything else is a normal approach and landing. Just double the normal approach power setting on the one working engine. Its all the "what-if" stuff that gets a pilot thinking.
In real life one-engine stuff is pretty easy especially since airline pilots constantly train these scenarios all the time. Its the real odd-ball situations that can get a bit tricky.