Wiring a relay for mains power
There are two aspects to this:

(1) You need a circuit to drive the coil of the relay. The easiest way to do this is to use a BJT transistor to control the current through the relay coil. The 3k3 resistor (3300 Ohm) is to limit the current from the microprocessor's output pin into the base of the transistor. The voltage (+V) driving the coil can be much higher than the supply to the microprocessor. Typical coil voltages for power-switching relays are 12 or 24VDC. It looks like you have a 12V relay, so you need to have +V = 12V. 

The 1N4004 diode is required to protect the transistor from flyback voltages when you turn off the relay. If you leave out the diode, your transistor will be hit with extremely high voltages (could be 100's of volts if it's a fast-acting transistor) and it will be destroyed in a puff of smoke.

I've suggested a 2N2222A transistor. Make sure it can handle the current that will flow through the relay coil.

(2) As you've bought the relay at Radio Shack, I'll assume you are in the USA. At a minimum, you will need to use the relay to cut or connect the "line" wire (L) (the narrower slot on a polarized plug). In a properly-wired home, the line wire carries 115VAC and the "neutral" wire (N) is near-ground. Given that you cannot guarantee that a home is properly wired (L and N could be reversed), and it is unwise to leave the "hot" wire connected to a load, it is best to use a double-pole relay to open/close BOTH the line and neutral wires. For European users, you will definitely want to cut both wires with a DP relay as there are both "Y" and "delta" phase configurations used in different countries, and both wires may be "hot".

Your relay is a single-pole relay, so it's not ideal for this application (unless you trust the wiring it will be use with).

Finally, I would recommend using the normally-open contacts of the relay. This means that your circuit must actively close the circuit (energize the relay). If something goes wrong with your control circuit, it is most likely to stop driving the transistor and hence cut power to the relay and load. It's safer this way.

Don't forget to wire together all the grounds for safety!