The first step is to install the Arduino IDE, which can be found on Arduino's website. This is where you will write code for the Arduino and upload it to the board. It is, without doubt, one of the most vital components for running an Arduino, second only to the board itself.
Once the IDE is downloaded, the board type must be selected under the "Tools" menu. Simply go to "Board," select whichever board is to be programmed, and move on to plugging the board into your computer. After the board is plugged in and an LED or two has lit up on the board, go to the "Tools" tab again and go to "Port." Select the port that is not "COM 1" or "Serial Ports." If none appear, try "COM 1" and begin uploading the desired code. If it pops up an orange bar at the bottom of the screen which reads "Problem uploading to board," unplug the Arduino and plug it back in while watching the "Port" portion of the "Tools" menu until a different COM port shows up, then select the new COM port.
Now comes my favorite part: writing the code! Most beginning Adruino users start with the following simple program:
void setup() { //The setup which allows the rest of the code to function
pinMode(9, OUTPUT); //Sets which pin is in use and what mode the pin is in
} //Ends the setup
void loop() { //Loops everything after the bracket
digitalWrite(led, HIGH); //Turns on the LED
delay(1000); //Sets the amount of time the LED is on in milliseconds
digitalWrite(led, LOW); //Turns off the LED
delay(1000); //Sets the amount of time the LED is off
} //Ends the loop
Once the code has been written, hit the arrow or go to "File" and hit "Upload."
Building the actual circuit is fairly easy with the most common Arduino, the Arduino Uno: turn off the Adruino by unplugging it, find a 220 Ohm resistor, an LED of any color (as long as it can run off of 5V), and connect the long leg on the LED to the resistor and the short leg to ground. Then wire the non-LED leg of the resistor to whichever Digital pin was chosen, which is shown under pinMode (pin 9 in this example). Power up the Arduino and voila! A blinking LED!