user-1: I am having a problem measuring the voltage with a multimeter. I am not sure if arduino is even sending out a voltage from the Pin. 
I will try to create a really basic circuit drawing for reference. (Drawing attached).

What I am trying to do is to measure with a Multimeter the Voltage (or current) across the alligator clips. 
I will attach the code below:
//Code Section Start//

int ledPin = 13;                 // LED connected to digital pin 13

void setup()
{
  pinMode(ledPin, OUTPUT);      // sets the digital pin as output
}

void loop()
{
  digitalWrite(ledPin, HIGH);   // sets the LED on
  delay(10000);                  // waits for a second
}

//Code Section End//

Typically the digital write I believe will out put 5 volts and with a 1k Ohm resistor that is only 5mA current. I have heard Arduino can take up to 40mA currents so I don't think I am frying something. 
There are two weird things I have noticed. When I try other Pins like "int ledPin = 10;" The green light on the Arduino does not light up. It only lights up when I use pin 13. However, even using Pin 13 or any other pin, I cannot find a voltage or current with the Multimeter. I am using an Arduino Micro. 
Can someone please help me identify what I am doing wrong or some method of how to check what is wrong? So that I can have a complete circuit with a voltage I can measure.

user-1: As you have drawn it, the alligator clips are clamped together (shorted togther).  You reading the voltage "across" a shorted element in the circuit should yield ~0V (shorts by definition have no to very little resistance, meaning there should be no voltage across them).  In order to get your proper voltage reading, you should place the multimeter positive clip above the resistor (where the voltage drop is occuring).
Remember.  
Measure current THROUGH.
Measure voltage ACROSS.
p.s. if you're trying to alternate the pin, you should do something like DigitalWrite(pin10, digitalRead(pin10)!=HIGH); (if it's low, then the statement evaluates to true, setting the pin high, if it's high, then the statement evaluates to false, setting the pin low)

user34029: As you connected the alligator clips (from the image it seems that they are touching each other) you won't be able to measure anything.
This is how to connect a multimeter to read the current (A) and the voltage (V). You can consider the + of E as the pin 13 and the - as the ground

Remember that your code will not change the state of pin 13, it will be always high.
If you want to make the signal change try this on your void loop :
  digitalWrite(ledPin, HIGH);
  delay(10000); 
  digitalWrite(ledPin, LOW);
  delay(10000);  


-1: <p>I am having a problem measuring the voltage with a multimeter. I am not sure if arduino is even sending out a voltage from the Pin. </p>

<p>I will try to create a really basic circuit drawing for reference. (Drawing attached).</p>

<p><a href="https://i.stack.imgur.com/w6z9v.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/w6z9v.png" alt="Basic Ciruit Diagram"></a></p>

<p>What I am trying to do is to measure with a Multimeter the Voltage (or current) across the alligator clips. </p>

<p>I will attach the code below:</p>

<pre><code>//Code Section Start//

int ledPin = 13;                 // LED connected to digital pin 13

void setup()
{
  pinMode(ledPin, OUTPUT);      // sets the digital pin as output
}

void loop()
{
  digitalWrite(ledPin, HIGH);   // sets the LED on
  delay(10000);                  // waits for a second
}

//Code Section End//
</code></pre>

<p>Typically the digital write I believe will out put 5 volts and with a 1k Ohm resistor that is only 5mA current. I have heard Arduino can take up to 40mA currents so I don't think I am frying something. </p>

<p>There are two weird things I have noticed. When I try other Pins like "int ledPin = 10;" The green light on the Arduino does not light up. It only lights up when I use pin 13. However, even using Pin 13 or any other pin, I cannot find a voltage or current with the Multimeter. I am using an Arduino Micro. </p>

<p>Can someone please help me identify what I am doing wrong or some method of how to check what is wrong? So that I can have a complete circuit with a voltage I can measure.</p>
 -1: <p>As you have drawn it, the alligator clips are clamped together (shorted togther).  You reading the voltage "across" a shorted element in the circuit should yield ~0V (shorts by definition have no to very little resistance, meaning there should be no voltage across them).  In order to get your proper voltage reading, you should place the multimeter positive clip above the resistor (where the voltage drop is occuring).</p>

<p>Remember.  </p>

<p>Measure current THROUGH.</p>

<p>Measure voltage ACROSS.</p>

<p>p.s. if you're trying to alternate the pin, you should do something like DigitalWrite(pin10, digitalRead(pin10)!=HIGH); (if it's low, then the statement evaluates to true, setting the pin high, if it's high, then the statement evaluates to false, setting the pin low)</p>
 34029: <p>As you connected the alligator clips (from the image it seems that they are touching each other) you won't be able to measure anything.</p>

<p>This is how to connect a multimeter to read the current (A) and the voltage (V). You can consider the <code>+</code> of E as the pin 13 and the <code>-</code> as the ground</p>

<p><a href="https://i.stack.imgur.com/3jyKE.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/3jyKE.jpg" alt=""></a></p>

<p>Remember that your code will not change the state of pin 13, it will be always high.
If you want to make the signal change try this on your <code>void loop</code> :</p>

<pre><code>  digitalWrite(ledPin, HIGH);
  delay(10000); 
  digitalWrite(ledPin, LOW);
  delay(10000);  
</code></pre>
