How does a three phase motor work on a two phase power supply and how do you wire it up?

A three phase motor will not work on a 2-phase power supply, it needs a 3-phase power supply.

Two phase electrical services are no longer the standard for electrical distribution. You would need to get an expensive phase-changer to convert your normal single phase power supply to three phase. Depending on the power output you require from the motor, it can often be much cheaper to buy a suitable single phase motor, new or secondhand, instead of buying a phase-changer as the power supply for a three phase motor.

If you really do want use that three phase motor you may find it worthwhile to contact your electricity supplier first, to ask if they can install a three phase service for you to use and what the cost would be. Otherwise, after you have bought the expensive phase-changer unit, you may find out later that your electricity supplier could have upgraded your service to three phase for a lower cost!