The exact requirements are slightly different for JAR Ops and FAR, but the principle is the same.
1) The engine installation must be so that no failure of one engine can affect the continued safe operation of the other engine. This is a very powerful statement that defines fully separate fuel systems, fire zones, airframe sensors and lots more.
2) A detailed procedure must be written to allow an OEI (one engine inoperative) rejected takeoff within specified landback distance; a critical decision point where it is safe to continue takeoff after an engine failure; the ability to safely climb out at a specified gradient (JAR) or climb rate (FAR) and accelerate to Vy; and the ability to achieve a climb rate at least 1000 feet above the takeoff point. For FAR the climb rate must be 150 feet per minute, JAR OPS allows some variance.
3) The procedures must provide a means of determining the combination of maximum weights, altitude and outside temperature to achieve the performance in 2 above.
4) The procedures must allow adjustment for changes in configuration and airframe systems operation to assure the performance in 2. This means that anti-ice, rotor de-ice, electrical loads, heater operation, doors open, and the like must all be accounted for in the procedures, if they are allowed in Cat A (JAR OPS 3) operations.
5) The procedures must be able to be performed by pilots of average skill, and no adjustment of engine controls is allowed for several seconds after the initial engine failure.