EFATO is a pilots' acronym standing for Engine Failure After Take Off. This is a very nasty thing to happen to you, as you are normally very low and going rather slowly when it does. It is identifiable normally by noise, such a bang or spluttering, and a loss of engine revs. Is there is only a slight loss of revs, then the failure is only partial, and so different drills must be carried out. Partial engine failure should not be confused with carburettor icing.
The standard drills for coping with a total EFATO are (in a propellor aircraft) to put the nose down to gain about 60 - 70 knots (depends on the type of aircraft), and then, is there is time, carry out the checks FIRMP. These stand for:
Fuel. Check whether there is fuel in the tank, but turn the pump off.
Ignition. Turn the engine off.
Radio. Make a MAYDAY call, stating, if possible, your intended landing patch (just pick a nice big field).
Main switch. This must also be turned off.
Propellor. Feather the prop to give a smoother glide (assuming your aircraft has prop feathering).
In the event of a partial engine failure, FIRM drills must be carried out, but everything should be left on, as you want the engine to run for as long as possible.
However, in no event should doing the drills come before landing safely.
One final horror story about learning EFATO drills: a cadet was up with his instructor, who pulled the throttle out and said 'The engine's failed'. The cadet pushed it back in, saying 'No it hasn't'. Then it really did.