Hall Effect Current Sensor Wiring
Looking at the datasheet the output is +/- 4 volts, so this is not suitable to connect directly to the Arduino, because the input pin will not tolerate -4 V.

I am no Hall Effect sensor expert, but a quick search on Google showed another potential problem: If you are planning to measure AC current, and you try to sample the output on the Arduino, the reading will average out to zero (half of the time positive, half of the time negative).

What may help - and this is a bit of a guess - is to put a diode in series with the sensor output, oriented so that you only get the positive pulses. That is, the anode connected to the Hall Effect sensor, and the cathode (with the black line) on the Arduino side.

Then you probably want to smooth the voltage so you can read the average voltage with the ADC converter, rather than what it is at a particular millisecond. A low-pass filter will take an average, which you can then read with analogRead.

Something like this:





I made up that circuit driven by a signal generator (8 V peak to peak, i.e. +/- 4 V) and found a 400 mV drop over the diode using a 1N4148 normal diode, and a 160 mV drop using a BAT85 Schottky diode.

With a 3 V peak-to-peak signal the voltage drop with the Schottky diode reduced to 120 mV, so it wasn't totally linear.



As Majenko pointed out, there is a voltage drop over the diode. You can make a Precision Rectifier out of an op-amp and a few other parts, like this:



This avoids the problem of the voltage drop (put this in place of the diode in the earlier circuit).

If the signal is AC then the smoothing circuit I described above will only give you an average voltage, not a peak one. You may want to sample rapidly in order to find the peak values.