Gather all required parts. 

Now you need to disassemble your old phone so that you will have access to the vibration motor connections. I have attached a video of disassembly of Nokia 3310. But the procedure will be same for almost all basic phones.Open one by one till you reach the main PCB. There you can see a vibration motor inside.

Vibration motor: It is used to provide haptic feedback to the user when a message or call comes. In vibration motors, there are two types,

1. Coreless motor with an unbalanced weight on the shaft. This results in change in moment of inertia resulting in wobbling and hence the vibration.
2. Coin cell type vibration motor which is sealed. 

We have to find the connection points of vibration motors.
And solder these points with 2 wires for extending it. Pretty much every basic phone has a vibration motor either of two types.

Connect these wires to one of the GPIOs of Arduino. Here I'm using pin number A0. And negative pin to ground. LCD connections are as usual. 
Relay module signal pin to pin number 4 and VCC, GND to Arduino's VCC and GND. You can use jumper wires for the connection here I have made a perf board circuit by soldering all components.

Here I will read the analog port and look for a high signal. And switch the pins accordingly. I have written everything in comments and code is self-explanatory. Whenever it reads a certain voltage at analog pin it activates the switch. This switch can be deactivated by again calling or by sending an SMS.

#include <LiquidCrystal.h>
int sensorPin = A0;    // select the input pin to the phone's vibration pin positive
int RelayPin = 4;      // select the pin for the Relay
int sensorValue = 0;  // variable to store the value coming from the phone
int sta = 0;
LiquidCrystal lcd(7, 8, 9, 10, 11, 12);

void setup() {
  lcd.begin(16, 2);
  // declare the ledPin as an OUTPUT:
  pinMode(RelayPin, OUTPUT);
  digitalWrite(RelayPin, HIGH); //Active low relay
}

void loop() {

  sensorValue = analogRead(sensorPin);

  if (analogRead(A0)>200)// When vibration motor is ON it is giving around 1.5V at the leads.
  {
    sta = sta + 1;
   
  }
  
    if (sta % 2 == 0)
    {
      lcd.clear();
      digitalWrite(RelayPin, HIGH);
      lcd.setCursor(0, 1);
      lcd.print("SWITCH OFF");
     delay(1000);// To avoid multiple on times while receiving message

    }

    if (sta % 2 != 0)
    {
      lcd.clear();
      digitalWrite(RelayPin, LOW);
      lcd.setCursor(0, 1);
      lcd.print("SWITCH ON");
      delay(1000);// To avoid multiple on times while receiving message

    }
}
  

Here I have attached a working video how the whole process works. I hope you enjoy recycling your old phone for a good purpose. 
Applications of this project are following:
1. Actuation of a pump set in an agricultural land 
2. Switching your room heater before going home. 
3. Switching your water heater for bathing 
4. Turning off the main switch of your home remotely.
And many more. Let me know if you guys find out anything else. 

The best part is you can trigger these switches from any part of the world where there is network access. 

I just wanted to show my old design of switching circuit. Back in those days i.e when I was in 11th grade I didn't have access to a computer and I never knew about microcontroller. Everything was analog. I have uploaded a video about my switching mechanism. Here I had used a DC motor to get the signal from the phone. When call or message comes this will rotate the motor in one direction and motor's gear rotates a rack of gear which presses a soft push button which I had extracted from a DVD drive. When the pushbutton is pressed it completes the circuit leading to the switching on of small DC pump set (Extracted from Car's wiper water supply).
This supplies water to the field in my demo.Then a water level controller circuit based on opamp senses the moisture level and when it crosses the threshold, it used to spin back the DC motor in other direction releasing the push button. This was the total control system I used in my older project.