Turning off and on well pump
There are two different methods to choose between.  

Method 1: pressure switch turns the pump on an off.  This method is most often used when the pump supplies water to more than just your irrigation system, or if you want to have a standard water faucet that always has water on demand.  

With this method you need a small storage tank (20-30 gallon, perhaps more depending on the flow rate (how fast the irrigation system can use water) to stabilize pressure and give the system water to use while the pump starts up.  When water use starts, the drop in pressure triggers a pressure switch which starts the pump at min pressure, and the same pressure switch shuts the pump off when pressure reaches a max.  Googling your pump it has a pressure switch attached to the side of the pump.

Method 2: Pump start relay controls the pump.  In this case case your pump will be controlled by the irrigation controller.  Bypass the built on pressure switch on the pump, and use a pump start relay compatible with your irrigation controller instead.  The low voltage side of the relay connects to the master valve/pump start relay terminals on your irrigation controller.  The irrigation controller starts and stops the pump when it runs.  Typically no storage tank is used in this setup.

Method 2 is simpler to install but doesn't allow for on-demand use of water (turning on a faucet).

Hint: Your pump is a dual voltage pump, 120/240.  Wire it up at 240V, it will run cooler, last longer and cost half as much to operate.