One (of many) ways to do this is use an FM radio for the receiver and purchase a low cost (less than $10) FM wireless transmitter kit. You can also look thru postings here for schematics and parts lists for the wireless transmitter. If you have a good junkbox (or a friend who does) you might have enough stuff on hand. Here in US very low power transmission of this type is allowed under some conditions - not sure about other countries. Doing the same thing on AM broadcast band is another choice.
As implied in the previous paragraph, there are many postings about this stuff. Note that lack of power, frequency drift, susceptability to interference, reliability and other undesireable traits are more likely with simpler, low cost solutions. Improved performance and reliability is obtained with increasing complexity (and cost). Realize that my "benchmark" or starting point would be simple, well designed and constructed circuits - I am not an advocate of making things too complex but you'll only get out what you put in.
Note that there are some transmitter modules and reciever modules (around 432 mHz) intended for short distance data transmitting and reception. I've not used these but they do look fairly simple - as I recall they were about $5 each.