What type of plug do I need to switch on a VL-CSH07G LED?
Ideally, You need a dedicated led driver with constant current. You get the current in milliamps mA from the line "Power Consumption"  and you get the voltage in V from the line "Operating Voltage". The led driver you get will need to be able to provide 700mA at 3.2V and no more. You could limit that down to 650 or 600 mA if you want a long life to the led.

The connector type is listed by part number on the line "Connector". You could cut it off and replace it with a different connector if you want.