This is all done by the Arduino and some python coding.
Step 1: Get the Parts
-5V DC Relay
-1N004 Rectifier Diode
-2N2222 NPN Switching Transistor
-CAT5e Wall Jack
PLEASE READ THIS:
Please note that to turn on and off the alarm clock you need one that you would normally turn on and off with a switch. You should NOT use an alarm clock that requires you to press a switch to turn it on and press a button to turn it off.
Step 2: Hack the Alarm Clock
First take apart your alarm clock and find were the switch is. Get to where the switch is and solder two wires to that. Now you can take out were the old button was and route the wire along the alarm clock. Then take some CAT5e, strip the end and then use the blue pair and connect them to the two wires that we soldered to the alarm clock. Now bend the other pairs on the CAT5e cable back a little so now you can use them to hold the wire in.
Now you have successfully hacked your alarm clock.
If you have ran into trouble here read the bottom of the first page on this instructable.
Step 3: The Relay Circuit
I have put the image of a sort of like schematic thing below. If you have any question just post them below.
Solder it all into your breadboard and then make wires for your Arduino.
IMPORTANT NOTICE: Do NOT solder directly to the Arduino. Solder to a wire and then when your done soldering connect that to the Arduino.