user11823: I got a copy of Arduino from a local retailer here (it's a local copy and I'm pretty confused with how the pins actually work).
I know basic electronics so far, there should be two pins for every node one acting as the negative terminal and other as the positive terminal. If I were to connect an LED with my Arduino board which pins would I be utilizing? 
Here let me tell you how pins are arranged on mine:
IOREF                                                                         GND                                  

                                         13  
RESET                                                                         12  
3.3V     //this left group marked power                                        .
5V                                  //right group marked PWM                   2
GND            //right groupmarked communication                          TX0 -1  
GND                                                                       RX0- 0                                   


V1N                                                                       TX3-14       
                                                                         RX2 -15
A0                                                                         ..
A1                                                                      SCL -21
..   //THIS left GROUP MARKED ANALOG IN
A7


A8
A9 //I believe it is part of the above group
..
A14
A15

     //the pins below marked DIGITAL
     52-50-`48-46...........................................................22`


user4143: Any IO pin can be set to either be an input, where it reports to your program if the voltage present on that pin (relative to ground) is above or below a certain threshold (HIGH or LOW voltage), or it can be an output, where it can either be set to be a HIGH output (pin is connected internally to +5V) or a LOW output (pin is connected internally to GND).
To drive an LED you would connect one side of a small resistor (say 470Ω) to any IO pin you choose.  The other side of the resistor would connect to the anode of the LED.  The cathode of the LED would then connect to ground.  When you set the IO pin to HIGH it will provide 5V to the LED through the resistor (which is needed to limit the current as the LED is a non-linear, current driven, component) and the circuit is completed by the return path through ground.

Note that you must not exceed 40mA going into or out of any IO pin, and you should not exceed 25mA going into or out of any IO pin.  The total current going into or out of all IO pins must not exceed 200mA.

user10794: 
there should be two pins for every node one acting as the negative terminal and other as the positive terminal. 

No, there is one pin per node, and a common "Ground" pin which is the negative terminal. On your Mega2560 are 5 ground pins (effectively equivalent because they are connected). They are circled on the photo below, and marked GND on the board.


As Majenko says in his answer you must use a resistor in series with any LED you connect, or you will damage both the LED and the processor.
You may find a "breadboard" handy for making connections, most prototyping boards have a long connected strip for sharing the Ground wire between different places, like this:

The continuous blue lines indicate pins which are connected together (for Ground) and the continuous red lines are connected together for +5 V (usually).


Btw can you tell me why there are two pins on the bottom horizontal row? 

Just for convenience. You often want an extra ground pin, for example if you are trying to connect up two LEDs.

Secondly, yes each pin can be set as input or output but is there any specific difference in the type of pins?

Some of the pins can optionally be used for extra hardware-supported features.

PWM: Pulse-width-modulated output
COMMUNICATION: Serial input/output (4 serial ports)
ANALOG IN: Analog-to-digital converter (ADC) input
DIGITAL: Digital (not analog) input/output
SDA/SCL: I2C communications
Pins 50-53: SPI communications (not marked on the board)

However all pins, as you noted, can - if you wish - be used for digital input or output.

11823: <p>I got a copy of Arduino from a local retailer here (it's a local copy and I'm pretty confused with how the pins actually work).</p>

<p>I know basic electronics so far, there should be two pins for every node one acting as the negative terminal and other as the positive terminal. If I were to connect an LED with my Arduino board which pins would I be utilizing? </p>

<p>Here let me tell you how pins are arranged on mine:</p>

<pre><code>IOREF                                                                         GND                                  

                                         13  
RESET                                                                         12  
3.3V     //this left group marked power                                        .
5V                                  //right group marked PWM                   2
GND            //right groupmarked communication                          TX0 -1  
GND                                                                       RX0- 0                                   


V1N                                                                       TX3-14       
                                                                         RX2 -15
A0                                                                         ..
A1                                                                      SCL -21
..   //THIS left GROUP MARKED ANALOG IN
A7


A8
A9 //I believe it is part of the above group
..
A14
A15

     //the pins below marked DIGITAL
     52-50-`48-46...........................................................22`
</code></pre>
 4143: <p>Any IO pin can be set to either be an input, where it reports to your program if the voltage present on that pin (relative to ground) is above or below a certain threshold (HIGH or LOW voltage), or it can be an output, where it can either be set to be a HIGH output (pin is connected internally to +5V) or a LOW output (pin is connected internally to GND).</p>

<p>To drive an LED you would connect one side of a small resistor (say 470Ω) to any IO pin you choose.  The other side of the resistor would connect to the anode of the LED.  The cathode of the LED would then connect to ground.  When you set the IO pin to HIGH it will provide 5V to the LED through the resistor (which is needed to limit the current as the LED is a non-linear, current driven, component) and the circuit is completed by the return path through ground.</p>

<p><a href="https://i.stack.imgur.com/SlqIV.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/SlqIV.png" alt="enter image description here"></a></p>

<p>Note that you <em>must not</em> exceed 40mA going into or out of any IO pin, and you <em>should not</em> exceed 25mA going into or out of any IO pin.  The total current going into or out of <em>all</em> IO pins <em>must not</em> exceed 200mA.</p>
 10794: <blockquote>
  <p>there should be two pins for every node one acting as the negative terminal and other as the positive terminal. </p>
</blockquote>

<p>No, there is one pin per node, and a <strong>common</strong> "Ground" pin which is the negative terminal. On your Mega2560 are 5 ground pins (effectively equivalent because they are connected). They are circled on the photo below, and marked <strong>GND</strong> on the board.</p>

<p><a href="https://i.stack.imgur.com/EWFnD.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/EWFnD.jpg" alt="Mega2560 board"></a></p>

<hr>

<p>As Majenko says in his answer you must use a resistor in series with any LED you connect, or you will damage both the LED and the processor.</p>

<p>You may find a "breadboard" handy for making connections, most prototyping boards have a long connected strip for sharing the Ground wire between different places, like this:</p>

<p><a href="https://i.stack.imgur.com/ArXKq.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ArXKq.jpg" alt="Prototyping board"></a></p>

<p>The continuous blue lines indicate pins which are connected together (for Ground) and the continuous red lines are connected together for +5 V (usually).</p>

<hr>

<blockquote>
  <p>Btw can you tell me why there are two pins on the bottom horizontal row? </p>
</blockquote>

<p>Just for convenience. You often want an extra ground pin, for example if you are trying to connect up two LEDs.</p>

<blockquote>
  <p>Secondly, yes each pin can be set as input or output but is there any specific difference in the type of pins?</p>
</blockquote>

<p>Some of the pins can optionally be used for extra hardware-supported features.</p>

<ul>
<li>PWM: Pulse-width-modulated output</li>
<li>COMMUNICATION: Serial input/output (4 serial ports)</li>
<li>ANALOG IN: Analog-to-digital converter (ADC) input</li>
<li>DIGITAL: Digital (not analog) input/output</li>
<li>SDA/SCL: I2C communications</li>
<li>Pins 50-53: SPI communications (not marked on the board)</li>
</ul>

<p>However <strong>all</strong> pins, as you noted, can - if you wish - be used for digital input or output.</p>
