Common usage of a three pole breaker is for use on a three phase distribution panel. Single phase distribution panels only use two pole breakers for a 240 volt load.
Remember that the breaker must protect the conductors that connect to the load. If you want to try and use a three pole breaker in a single phase panel just because you have the breaker, this is not a good idea even if it will fit.
Purchase the proper single phase two pole breaker to match the wire size and the amperage of the connected 240 volt load. Keep in mind that connected 240 volt motor loads have to be sized to 250% of the motor's full load amperage.
By doing what you want to do and a fault occurs from this type of installation your insurance company might not cover the damage that it would cause.
If the distribution panel is three phase then just connect the two load wires to any two of the three poles on the breaker.
the easiest way to tell, is the shunt trip breaker will actually take up 4 spaces in your panel. the 4th space will have a neutral wire coming out of it, along with a lug for power INPUT. when voltage is applied to the shunt trip, it will cause the other 3 poles to open by tripping the breaker.
A NEMA 14-30P is a plug. A 14-30R is a 3pole 4wire grounding receptacle for 125/250 volts. To wire the receptacle connect a three wire cable's red and black wires to terminals X and Y respectively. Connect the cable's white wire to the W terminal and the ground wire to the G terminal.
Phases in AC refer to the number of sine waves of alternating current used to generate the average voltage. In 2 phase, two opposing sine waves are overlapped to give the average voltage delivered, eg 240V in household supplies. In 3 phase, three sine waves are overlapped to produce a more consistent average voltage.