user38031: I uploaded the Blink sketch (from the ESP8266 examples, in the Arduino IDE) successfully. 
Depending on which wire configuration I am using two different things happen:
wiring 1:
CH_PD -> 3.3V
VCC -> 3.3V
RST -> GND
GPI02 -> LED
GND -> GND

wiring 2:
VCC -> 3.3V
RST -> GND
GPI02 -> LED
GND -> GND


There are TX/RX lines in the picture from when I was flashing - they aren't being used for running the sketch.
With wiring 1 the LED stays on (doesn't blink) - I was wondering if this was because I still had the VCC -> 3.3V connected. So I disconnected that, which gives way to wiring 2.
With wiring 2 the LED doesn't come on at all, it is the same as wiring 1 except without VCC -> 3.3V.
Why is it constant when 3.3V is going to VCC, and constantly off when I disconnect it? Why doesn't it blink using wiring 2?
UPDATE
A diagram as requested, sorry it was my first time doing this:

Code:
/*
 ESP8266 Blink by Simon Peter
 Blink the blue LED on the ESP-01 module
 This example code is in the public domain

 The blue LED on the ESP-01 module is connected to GPIO1 
 (which is also the TXD pin; so we cannot use Serial.print() at the same time)

 Note that this sketch uses LED_BUILTIN to find the pin with the internal LED
*/

void setup() {
  pinMode(LED_BUILTIN, OUTPUT);     // Initialize the LED_BUILTIN pin as an output
}

// the loop function runs over and over again forever
void loop() {
  digitalWrite(LED_BUILTIN, LOW);   // Turn the LED on (Note that LOW is the voltage level
                                    // but actually the LED is on; this is because 
                                    // it is acive low on the ESP-01)
  delay(1000);                      // Wait for a second
  digitalWrite(LED_BUILTIN, HIGH);  // Turn the LED off by making the voltage HIGH
  delay(2000);                      // Wait for two seconds (to demonstrate the active low LED)
}


user37418: I can't comment as my karma is too low so if I am wrong please just someone let me know and I'll simply delete.
I thought that the RST pin being pulled to ground resets the chip, if this is the case surely in your setup you are constantly reseting your chip, so it won't do anything. My understanding is that you should have the reset pin pulled up to 3.3V with a 10K resistor. 

user27653: You should connect Vcc to 3.3V, because that's how the ESP8266 is powered.
RST is active-low reset and should be pulled to 3.3V

38031: <p>I uploaded the Blink sketch (from the ESP8266 examples, in the Arduino IDE) successfully. </p>

<p>Depending on which wire configuration I am using two different things happen:</p>

<p><code>wiring 1</code>:</p>

<pre><code>CH_PD -&gt; 3.3V
VCC -&gt; 3.3V
RST -&gt; GND
GPI02 -&gt; LED
GND -&gt; GND
</code></pre>

<p><code>wiring 2</code>:</p>

<pre><code>VCC -&gt; 3.3V
RST -&gt; GND
GPI02 -&gt; LED
GND -&gt; GND
</code></pre>

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

<p>There are TX/RX lines in the picture from when I was flashing - they aren't being used for running the sketch.</p>

<p>With <code>wiring 1</code> the LED stays on (doesn't blink) - I was wondering if this was because I still had the VCC -> 3.3V connected. So I disconnected that, which gives way to <code>wiring 2</code>.</p>

<p>With <code>wiring 2</code> the LED doesn't come on at all, it is the same as <code>wiring 1</code> except without VCC -> 3.3V.</p>

<p>Why is it constant when 3.3V is going to VCC, and constantly off when I disconnect it? Why doesn't it blink using <code>wiring 2</code>?</p>

<p><strong>UPDATE</strong></p>

<p>A diagram as requested, sorry it was my first time doing this:</p>

<p><a href="https://i.stack.imgur.com/Z0OgR.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Z0OgR.png" alt="enter image description here"></a></p>

<p>Code:</p>

<pre><code>/*
 ESP8266 Blink by Simon Peter
 Blink the blue LED on the ESP-01 module
 This example code is in the public domain

 The blue LED on the ESP-01 module is connected to GPIO1 
 (which is also the TXD pin; so we cannot use Serial.print() at the same time)

 Note that this sketch uses LED_BUILTIN to find the pin with the internal LED
*/

void setup() {
  pinMode(LED_BUILTIN, OUTPUT);     // Initialize the LED_BUILTIN pin as an output
}

// the loop function runs over and over again forever
void loop() {
  digitalWrite(LED_BUILTIN, LOW);   // Turn the LED on (Note that LOW is the voltage level
                                    // but actually the LED is on; this is because 
                                    // it is acive low on the ESP-01)
  delay(1000);                      // Wait for a second
  digitalWrite(LED_BUILTIN, HIGH);  // Turn the LED off by making the voltage HIGH
  delay(2000);                      // Wait for two seconds (to demonstrate the active low LED)
}
</code></pre>
 37418: <p>I can't comment as my karma is too low so if I am wrong please just someone let me know and I'll simply delete.</p>

<p>I thought that the RST pin being pulled to ground resets the chip, if this is the case surely in your setup you are constantly reseting your chip, so it won't do anything. My understanding is that you should have the reset pin pulled up to 3.3V with a 10K resistor. </p>
 27653: <p>You should connect Vcc to 3.3V, because that's how the ESP8266 is powered.
RST is active-low reset and should be pulled to 3.3V</p>
