How do start and stop a 3 phase 480 volt AC industrial motor with 24V DC? The simple answer is by using a motor controller Many types of motor controllers are available in various types and Styles in industrial control. all motor controllers are designed to keep the motor from being energized until the controllers told to. Once activated, current can pass to the motor which energizes the motor windings and starts motor rotation. Activation of the motor controller is typically accomplished within an electromechanical device built into the controller also known as a contractor.

Motor controllers may referrers to motor starters. These devices are most often offered in a single unit with Circuit disconnecting, including contactor and motor protection actuators like overload protection.
Motor controllers can be classified by starting method and starting type.
Starting methods

The first starting type is the full voltage non-reversing motor controller as the name implies when the controllers single contactor actuates this motor controller type also known as FVNR allows the full line voltage to pass to the motor. With an FVNR motor controller, the position of the line phases is fixed in the motor, so the motor can be operated in one rotational direction.

In FVNR can be thought of as an across the line controller in a full voltage reversing motor controller the controller has two separate actuated states won the operator motor in the forward direction and one state to allow the motor to operate in the reverse direction. This is accomplished by adding a second contactor, which swaps the position of two of the phases.

This reverses the magnetic field in the motor windings to be reversed causing the motor to spin in the opposite direction special physical safeguards are in place to prevent the actuation of both contactors at the same time which would be very damaging.

The third type of motor starting method is called reduced voltage starting 
large Motors can have a very high starting current that may be harmful to the motor or the motor controller itself to limit the amount of starting current to these motors this type of motor controller applies a reduced voltage to the motor when it first starts
There are several ways to accomplish this searches autotransformer start Delta and soft starter 

The last type of motor starting method is multi-speed.
Multi-speed motor controllers use solid-state or transforming to allow motors to be controlled at different speeds

Motor starter types.

The first is manual motor actuation which requires an operator to switch the motor on and off due to safety considerations manual motor starting is limited to Motors of less than 7KW. But they can be used on single or three-phase applications. Magnetic motor starters or direct online starters (DOL) for the most common Singlespeed started type for magnetic starters at the PLC digital output a push button or a selector switch is used to pull in a coil which magnetically holds the start of contact closed allowing current to pass to the motor magnetic motor starter to use with FVNR and full voltage reversible motor controllers.

 autotransformer motor starters are commonly used in reduced voltage starting applications especially with large Motors when the motor starts 2 contacts pull in

One of these contractors energizes a transformer circuit, and the other forces the transformer into a star configuration. The tapped output from the transformer is connected to the motor leads. When the motor reaches 85 the 90% of full voltage the star contactor opens. Then the transformer then acts as a choke to limit the voltage in the current to the motor. the main contractor then closes

Star/Delta reduce voltage motor starting is related to Autotransformers. starting in that three separate contactors are used in the motor control scheme in Star Delta the motor is started in the star configuration which starts the motor at about one-third of the rated motor current. After the motor spins near full speed, the motor is switch to the Delta configuration.

Another method used for limiting starting current source starters is solid-state Electronics to limit the start of voltage and current. With a soft starter, the voltage is gradually increased during the motor start out. This allows the motor to slowly accelerate and Gain speed in a controlled fashion. 

A variable frequency drive or VFD is similar to a soft starter but allows the speed of the motor to be varied by varying the frequency of the output to the motor because the voltage is also regulated in the process. The start-up current is also reduced with the use of a VFD.

Three phase motor forward and reverse circuit with Latch ON

MPROT is motor protection relay and basically works like stop push button

As it can be seen simply Forward interlocked with reverse (REV NC) and use latch (FWD NO)