All of the code and instruction provided is done so with no guarantee of success. I've bugtested the code to the best of my ability, and it should work in most cases, but certain things can throw it off. Details of such are within.
Step 1: Required Pieces/Parts for the Project
(1) Arduino Uno board
(1) Breadboard (I used a MakerShield prototyping shield instead, but a breadboard works just as well, albeit less compact)
(1) LED, your choice of color
(>12) Breadboard cables
(1) 16x2 Character LCD display, compatible with the LiquidCrystal library (works with larger LCD's with tweaking)
(1) Potentiometer, preferably 10K ohms.
(1) USB to USB-B cable (standard USB-to-Arduino cable)
Step 2: Wiring up the LCD and the LED
Picture is from http://arduino.cc/en/Tutorial/LiquidCrystal. Make sure you test it using the "Hello World!" program described. The screen may need to have the contrast turned all the way up for it to display properly.
The LED just goes in digital pin 13 and the GND pin next to it. Make sure the polarity is correct (Longer leg should be the + leg, short legs goes to ground).