High Saravanan,
Imagine that the coils in the schematic are the coil inside the motor. The value of each capacitor runs from 80uF to 150uF per HP. The purpose of the switch it to minimize the delays caused by excess capacitance when the motor is already running. The delays could produce too much vibration.
The common connection of most 3-phase motor is Y-connection of the coil. You can observe it as you open the supply terminal of the motor(6 terminals, 2 side with 3 terminals per side. The one of its side is from the 3-phase supply and the other probably to the 3-phase connection of the motor). The side of 3-phase terminal connected to the motor coils is probably connected with each other for the purpose of Y-connection. (Note: In case you will not find this 6 terminals try to make delta connections through simple wire connection or if you insist on supplying the 3rd phase supply, try to use a capacitor in between either one of the 2 live phase you have and connect it the 3rd phase supply. It is just for starting the motor and disconnect it when the motor is already running.)
The main problem of 3-phase motor is you need a high starting torque with 3 phase shifted supply so it can run. You can run 3-phase motor with 2-phase or 1-phase supply but it gives less power compared to the 3-phase supply.
In case you are still a bit confused try the article link below:
http://www.nerdylorrin.net/jerry/ThreePhase.htmlI hope it helps.
Good Luck
