I would like to know what the cheapest and easiest way to connect a three phase 2.2kW AC induction motor to a single phase 230V power supply is. Also, in this setup, how can the motor be started and stopped? Would there be a need for protection devices?
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The Steinmetz connection is probably the cheapest and easiest, but it only allows the motor to provide 70% of its rated power. See: 3 phase motor running on single phase using steinmetz delta connection
Powering the motor through a Variable Frequency Drive (VFD) allows the motor to provide rated power and also provides variable speed. That may be easier and the cost may be less than any other alternative other than the Steinmetz connection.
What is easiest depends to some extent on the experience of the person doing the conversion.
What is cheapest depends on the willingness and ability to scrounge up and use parts that are used and what materials can be cheaply obtained.
For more information on alternative methods, see: Single-phase to 3-phase conversion
A VFD would provide starting and stopping and protection against motor motor overload protection and ground fault of the motor lines. The input power feed to the VFD would require a circuit breaker or other disconnect means and branch circuit protection. Before purchasing a VFD it is advisable to download and read the manual.