Connect a sensor to Arduino without knowing much info about the sensor
You have linked to the datasheet of the sensor.

In the datasheet, look at the "Application Circuit" section. You must build this circuit. The sensor produces a very small electric current, and the application circuit is high-gain amplifier to translate that very small electric current to a varying voltage you can sample with the Arduino ADC.

Note on the circuit, the wire labled "To ADC" -- that is the part which you connect to your arduino.

As for calibration, the datasheet itself notes that the process is non-trivial, or that they can perform a calibration, for an additional fee, at the time you order a batch of sensors. Presumably their calibration will include the precise resistor values used to set the gain of the amplifier, and also an equation to associate PPM values to the analog voltage provided at the "To ADC" wire.

As for reading the circuit diagram (schematic), you may already know resistors and capacitors. For the other items, search online for the part numbers given, to find out what they are.

The datasheet also notes that the application circuit is available pre-built from the sensor manufacturer. You may want to contact them to determine how to purchase one for yourself.

Most electronics products have a datasheet that explains all you typically need to know about the device, such as it's operating parameter minima and maxima, typical values, typical outputs, etc. This sensor is no different, except that the calibration procedure is not described in great detail due to the complexity.