How to measure electrical conductivity using Arduino?
The answer is Three Dollar EC - PPM Meter [Arduino]. I tried it against a consumer level EC meter and got the same results after calibration. It's cheap and simple.



The only warning is that there is several scales in use to measure EC, so results may not be comparable between diferentes devices and you have to read carefully the EC recomendations for your water solution.

EC units

Electrical conductivity can be expressed using a number of different units, but the typical unit is siemens per meter2 per mole (S/m2/mole) or millisiemens per centimetre (mS/cm). The mS/cm unit is generally used in Europe as a guide to the concentration of nutrients in water. In North America, conductivity is converted into a count of the ions in the water using parts per million (which can also be converted into units including mg/l etc.). This is done by converting the EC into a value based on the ions contained in the solution. Fortunately, there is a fixed calculation for the relationship between all these units, which is given in the table below.



Code for the EC meter

/*
  ElCheapo Arduino EC-PPM measurments

  This scrip uses a common USA two prong plug and a 47Kohm Resistor to measure the EC/PPM of a Aquaponics/Hydroponics Sytem.
  You could modift this code to Measure other liquids if you change the resitor and values at the top of the code.

  This Program will give you a temperature based feed controller. See Read me in download file for more info.

  28/8/2015  Michael Ratcliffe  Mike@MichaelRatcliffe.com


          This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.


    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.


    You should have received a copy of the GNU General Public License
    along with this program.  If not, see .

    Parts:
    -Arduino - Uno/Mega
    -Standard American two prong plug
    -1 kohm resistor
    -DS18B20 Waterproof Temperature Sensor

    Limitations:
    -
    -

    See www.MichaelRatcliffe.com/Projects for a Pinout and user guide or consult the Zip you got this code from

*/

#include &lt;OneWire.h&gt;
#include &lt;DallasTemperature.h&gt;

//************************* User Defined Variables ********************************************************//

int R1= 1000;
int Ra=25;          //Resistance of powering Pins
int ECPin= A0;
int ECGround=A1;
int ECPower =A4;

//*********** Converting to ppm [Learn to use EC it is much better**************//
// Hana      [USA]        PPMconverion:   0.5
// Eutech    [EU]         PPMconversion:  0.64
// Tranchen  [Australia]  PPMconversion:  0.7
// Why didnt anyone standardise this?

float PPMconversion=0.5;

//*************Compensating for temperature ************************************//
// The value below will change depending on what chemical solution we are measuring
// 0.019 is generaly considered the standard for plant nutrients [google "Temperature compensation EC" for more info
float TemperatureCoef = 0.019; //this changes depending on what chemical we are measuring

//********************** Cell Constant For Ec Measurements *********************//
// Mine was around 2.9 with plugs being a standard size they should all be around the same
// But If you get bad readings you can use the calibration script and fluid to get a better estimate for K
float K=2.34;

//************ Temp Probe Related *********************************************//
#define ONE_WIRE_BUS 10          // Data wire For Temp Probe is plugged into pin 10 on the Arduino
const int TempProbePossitive =8;  //Temp Probe power connected to pin 9
const int TempProbeNegative=9;    //Temp Probe Negative connected to pin 8

//***************************** END Of Recomended User Inputs *****************************************************************//


OneWire oneWire(ONE_WIRE_BUS);// Setup a oneWire instance to communicate with any OneWire devices
DallasTemperature sensors(&amp;oneWire);// Pass our oneWire reference to Dallas Temperature.

float Temperature=10;
float EC=0;
float EC25 =0;
int   ppm =0;

float raw= 0;
float Vin= 5;
float Vdrop= 0;
float Rc= 0;
float buffer=0;

//*********************************Setup - runs Once and sets pins etc ******************************************************//
void setup()
{
    Serial.begin(9600);
    pinMode(TempProbeNegative , OUTPUT);  //seting ground pin as output for tmp probe
    digitalWrite(TempProbeNegative , LOW); //Seting it to ground so it can sink current
    pinMode(TempProbePossitive , OUTPUT); //ditto but for positive
    digitalWrite(TempProbePossitive , HIGH);
    pinMode(ECPin,INPUT);
    pinMode(ECPower,OUTPUT);//Setting pin for sourcing current
    pinMode(ECGround,OUTPUT);//setting pin for sinking current
    digitalWrite(ECGround,LOW);//We can leave the ground connected permanantly

    delay(100);// gives sensor time to settle
    sensors.begin();
    delay(100);
    //** Adding Digital Pin Resistance to [25 ohm] to the static Resistor *********//
    // Consule Read-Me for Why, or just accept it as true
    R1=(R1+Ra);// Taking into acount Powering Pin Resitance

    Serial.println("ElCheapo Arduino EC-PPM measurments");
    Serial.println("By: Michael Ratcliffe  Mike@MichaelRatcliffe.com");
    Serial.println("Free software: you can redistribute it and/or modify it under GNU ");
    Serial.println("");
    Serial.println("Make sure Probe and Temp Sensor are in Solution and solution is well mixed");
    Serial.println("");
    Serial.println("Measurements at 5's Second intervals [Dont read Ec morre than once every 5 seconds]:");
}

void loop()
{
    GetEC();          //Calls Code to Go into GetEC() Loop [Below Main Loop] dont call this more that 1/5 hhz [once every five seconds] or you will polarise the water
    PrintReadings();  // Cals Print routine [below main loop]
    delay(5000);
}

void GetEC()
{
    sensors.requestTemperatures();          // Send the command to get temperatures
    Temperature=sensors.getTempCByIndex(0); //Stores Value in Variable
    //************Estimates Resistance of Liquid ****************//
    digitalWrite(ECPower,HIGH);
    raw= analogRead(ECPin);
    raw= analogRead(ECPin);// This is not a mistake, First reading will be low beause if charged a capacitor
    digitalWrite(ECPower,LOW);

    //***************** Converts to EC **************************//
    Vdrop= (Vin*raw) / 1024.0;
    Rc = (Vdrop*R1) / (Vin-Vdrop);
    Rc = Rc-Ra; //acounting for Digital Pin Resitance
    EC = 1000/ (Rc*K);

    //*************Compensating For Temperaure********************//
    EC25  =  EC / (1+ TemperatureCoef*(Temperature-25.0));
    ppm=(EC25)*(PPMconversion*1000);
}


//***This Loop Is called From Main Loop- Prints to serial usefull info ***//
void PrintReadings()
{
    Serial.print("Rc: ");
    Serial.print(Rc);
    Serial.print(" EC: ");
    Serial.print(EC25);
    Serial.print(" Simens  ");
    Serial.print(ppm);
    Serial.print(" ppm  ");
    Serial.print(Temperature);
    Serial.println(" *C ");
};


Code for calibration

/*
  ElCheapo Arduino EC-PPM measurments Calibration

  This Script is used for calibration of the sensor and fine tuning of the Cell Constant K
  Submerge the sensor and temperature probe in the calibration solution and leave for a while so the temperature probe can settle
  Change the value of the calibration solution to suit the solutiton strength
  Stir the probe to make sure the solution is well mixed and upload the code to the arduino
  Open the terminal for an update of the estimated Cell Constant K [should be around 3] and use this new value in the main EC code.


  28/8/2015  Michael Ratcliffe  Mike@MichaelRatcliffe.com


          This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.


    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.


    You should have received a copy of the GNU General Public License
    along with this program.  If not, see .

    Parts:
    -Arduino - Uno/Mega
    -Standard American two prong plug
    -1 kohm resistor
    -DS18B20 Waterproof Temperature Sensor


    See www.MichaelRatcliffe.com/Projects for a Pinout and user guide or consult the Zip you got this code from

*/


//************************** Libraries Needed To Compile The Script [See Read me In Download] ***************//
// Both below Library are custom ones [ SEE READ ME In Downloaded Zip If You Dont Know how To install Use them or add a pull up resistor to the temp probe

#include &lt;OneWire.h&gt;
#include &lt;DallasTemperature.h&gt;

//************************* User Defined Variables ********************************************************//

float CalibrationEC = 0.762; //EC value of Calibration solution is s/cm

//##################################################################################
//-----------  Do not Replace R1 with a resistor lower than 300 ohms    ------------
//##################################################################################
int R1 = 1000;
int Ra = 25; //Resistance of powering Pins
int ECPin = A0;
int ECGround = A1;
int ECPower = A4;

//*************Compensating for temperature ************************************//
//The value below will change depending on what chemical solution we are measuring
//0.019 is generaly considered the standard for plant nutrients [google "Temperature compensation EC" for more info
float TemperatureCoef = 0.019; //this changes depending on what chemical we are measuring

//************ Temp Probe Related *********************************************//
#define ONE_WIRE_BUS 10          // Data wire For Temp Probe is plugged into pin 10 on the Arduino
const int TempProbePossitive = 8; //Temp Probe power connected to pin 9
const int TempProbeNegative = 9;  //Temp Probe Negative connected to pin 8

//***************************** END Of Recomended User Inputs *****************************************************************//


OneWire oneWire(ONE_WIRE_BUS);// Setup a oneWire instance to communicate with any OneWire devices
DallasTemperature sensors(&amp;oneWire);// Pass our oneWire reference to Dallas Temperature.


float TemperatureFinish = 0;
float TemperatureStart = 0;
float EC = 0;
int ppm = 0;

float raw = 0;
float Vin = 5;
float Vdrop = 0;
float Rc = 0;
float K = 0;
int i = 0;
float buffer = 0;

//*********************************Setup - runs Once and sets pins etc ******************************************************//
void setup()
{
    Serial.begin(9600);
    pinMode(TempProbeNegative , OUTPUT);  //seting ground pin as output for tmp probe
    digitalWrite(TempProbeNegative , LOW); //Seting it to ground so it can sink current
    pinMode(TempProbePossitive , OUTPUT); //ditto but for positive
    digitalWrite(TempProbePossitive , HIGH);
    pinMode(ECPin, INPUT);
    pinMode(ECPower, OUTPUT); //Setting pin for sourcing current
    pinMode(ECGround, OUTPUT); //setting pin for sinking current
    digitalWrite(ECGround, LOW); //We can leave the ground connected permanantly

    delay(100);// gives sensor time to settle
    sensors.begin();
    delay(100);
    //** Adding Digital Pin Resistance to [25 ohm] to the static Resistor *********//
    // Consule Read-Me for Why, or just accept it as true
    R1 = (R1 + Ra);

    Serial.println("ElCheapo Arduino EC-PPM measurments Calibration");
    Serial.println("By: Michael Ratcliffe  Mike@MichaelRatcliffe.com");
    Serial.println("Free software: you can redistribute it and/or modify it under GNU ");
    Serial.println("");
    Serial.println("Make sure Probe and Temp Sensor are in Solution and solution is well mixed");
    Serial.println("");
    Serial.println("Starting Calibration: Estimated Time 60 Seconds:");
};
//******************************************* End of Setup     
//************************************* Main Loop - Runs Forever ***************************************************************//
//Moved Heavy Work To subroutines so you can call them from main loop without cluttering the main loop
void loop()
{
    i = 1;
    buffer = 0;
    sensors.requestTemperatures();// Send the command to get temperatures
    TemperatureStart = sensors.getTempCByIndex(0); //Stores Value in Variable

    //************Estimates Resistance of Liquid ****************//
    while(i &lt;= 10) {
        digitalWrite(ECPower, HIGH);
        raw = analogRead(ECPin);
        raw = analogRead(ECPin); // This is not a mistake, First reading will be low
        digitalWrite(ECPower, LOW);
        buffer = buffer + raw;
        i++;
        delay(5000);
    };

    raw = (buffer / 10);

    sensors.requestTemperatures();// Send the command to get temperatures

    TemperatureFinish = sensors.getTempCByIndex(0); //Stores Value in Variable

    //*************Compensating For Temperaure********************//
    EC = CalibrationEC * (1 + (TemperatureCoef * (TemperatureFinish - 25.0))) ;

    //***************** Calculates R relating to Calibration fluid **************************//
    Vdrop = (((Vin) * (raw)) / 1024.0);

    Rc = (Vdrop * R1) / (Vin - Vdrop);

    Rc = Rc - Ra;

    K = 1000 / (Rc * EC);

    Serial.print("Calibration Fluid EC: ");

    Serial.print(CalibrationEC);

    Serial.print(" S  ");  //add units here

    Serial.print("Cell Constant K");

    Serial.print(K);

    if(TemperatureStart == TemperatureFinish) {
        Serial.println("  Results are Trustworthy");
        Serial.println("  Safe To Use Above Cell Constant in Main EC code");

    } else {
        Serial.println("  Error -Wait For Temperature To settle");
        Serial.print("Temp start=");
        Serial.print(TemperatureStart);
        Serial.print(" Temp end=");
        Serial.println(TemperatureFinish);
    }
}
//*************************** End Of Main Loop *******************************************************************//


EDIT:

Make sure to use a factory sealed male plug. If water get inside the plug, the voltage reading will be inaccurate.