To read the sensor properly you have to convert the output signal into something the Arduino can work with.
At full current the output will swing between +4V and -4V, and over-current will cause that to be nearer +6V to -6V. The frequency of that swing will be the frequency of the input voltage - so typically 50 or 60Hz.
The Arduino can only read between 0V and 5V, so you will need to convert the provided voltage to fit.
You need to first reduce the voltage by about a half, so it fits into +/- 2V, and then you need to add a 2.5V offset voltage to it so that it swings between 0.5V and 4.5V.
Once you have done that you then need to sample the incoming signal fast enough that you can get the peak values, from which you can then calculate the incoming current.
Often for this kind of thing you would use a simple voltage divider with an offset voltage applied to it, but the output impedance of the sensor (set by RL) is 10KΩ which is around the upper limit for the input impedance of the Arduino's input. A voltage divider that wouldn't adversely affect the output accuracy would be using resistors in the order of 1MΩ, which would be way too high for the ADC on the Arduino to be able to sample accurately.
So you need to buffer the signal with a high impedance buffer. That can be achieved most simply with an inverting op-amp circuit with a gain of 0.5. You want a rail-to-rail op-amp which is capable of running from a single supply voltage.
In this circuit the output current is converted into a voltage by the 10KΩ resistor RL. It is then AC coupled to the rest of the circuit through C1 which has to be high enough in value as to not reject the frequency you are working with (it acts like a high-pass filter). R1 and R2 set the gain of 50/100, or 1/2, so the voltage is halved. R3 and R4 form a voltage divider to provide a VCC/2 offset voltage into the non-inverting input of the op-amp. This is known as the virtual ground voltage and is the voltage the output of the op-amp will swing around.
The result is the input voltage inverted, halved and off-set by 2.5V, which can be read directly by the Arduino's ADC.
Note the magic word inverted there, though. The values you read will be upside down. Anything read above 512 from the ADC will equate to a negative voltage. Anything read below 512 will be a positive voltage. So it is necessary to first "invert" the reading, which can simply be done by subtracting it from 1023.
Then it's just a matter of sampling often enough and recording the peak (and negative peak) values over a short period. The faster you can sample the better your results will be.
From those peak values you can then do all sorts of calculations and things. You can use them "as is" to directly give you the "peak-to-peak" current, or calculate the RMS voltage to then give you the RMS current.