Here is a quick explanation of different start-up types of three-phase induction motors.
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Direct starting

It only needs a standard motor starter box, usually sold with thermal protections and a reversing system for rotation direction (by reversing 2 phases).
The relay power supply is taken in 2 phases or between phase and neutral.

The problem is the starting intensity, when the motor is wired in delta (6 to 8 times the nominal intensity).
It is then better to start in a star connection, and after to connect the motor in delta when the steady state is reached.

Star-delta start

The principle is the following: a contactor connects the motor in star, while the main contactor supplies the motor.
A timer starts, which reverses the coupling after few seconds.

Soft starter

In this case, the motor is connected in delta, and the starter limits the relation U/f to limit the torque and so the inrush current.

Finally, we use more and more often a variable frequency drive that handles the engine start, but also enables to vary the speed when operating.