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Easiest way is to go to a place like rentron.com or sparkfun.com and buy a pair of transmitter/receiver modules. You pretty much give them power, antenna, and the signal you want to transmit, and it takes care of the rest. At rentron.com they sell complete kits for their remote control modules.
Yeah, that circuit will work just great for turning something on by remote. You might want to replace the relay with a transistor if you're just turning something small on, it'd be cheaper and smaller.