OMG Questions, questions, qutestions... :)
My question is do I need to define what equals every number(What pins)or is that already defined?
The pins I suggested were just for the sake of having something to demonstrate the principles. Hook an arduino up to some buttons using it's input "pins" as I described and you'll see that it works. In reality, you could use any input method and just modify the code to suit your final design.
What is the serial port?
It's a serial communication interface included on all arduino boards. In reality you won't be using it in your final design. When you hook up your arduino to a computer you can monitor this for anything your program sends down it and have it display on your screen. The arduino IDE includes a "Serial Monitor" My code uses this as a stand in for your final display. In reality, this part would have to be rewritten to send the same information to your REAL display.
From here, I am going to hook up an rf remote panel (the one I want to use:http://www.ebay.com/itm/DC-12v-relay-6CH-wireless-RF-Remote-Control-Switch-Transmitter-Receiver-/121361951834?pt=Home_Automation_Controls_Touchscreens&hash=item1c41bc6c5a
There are cheaper ways of doing it, but in view of your limited experience in electronics, it may be one of the simpler solutions to implement. Yes, it should work.
. To clarify, I do not need to hook up anything to pin 1 correct?
Pin 1 is, internally (within the arduino circuitry) connected to the serial port. It's worth leaving this alone so that you can still use the serial port to communicate with the computer. It's a valuable tool to help work out what's going wrong (when things need to debugging).
And what is the UpdateTime for? What is the GND? What board should I use?
In the example code I posted, UpdateTime is simply a function that decrements the playing time remaining. It gets called once every second.
GND (short for Ground) is the negative side of the power supply on the arduino. There are a few pins on the arduino marked GND. In the example code I posted, the arduino detects it's input pins being connected to this (by the action of the button).