People around the world have transmitters and receivers in their homes already. In fact, many people have these devices without realising it. Another term for a "transmitter" and a "receiver" is a radio. These devices are the most basic levels of radios that send a signal out -- the transmitter -- and get a signal back -- the receiver. You can build your own basic radio at home.
Create a transmitter by making a rapidly changing current in a wire. This can be done by touching a wire to a battery and removing the wire from the battery. This will create a square wave that fluctuates between zero volts and 1.5 volts.
Create a more continuous -- or sine -- wave for your transmitter with a capacitor (a simple battery that stores electrons) and inductor (a wire coil that has magnetic properties). Connect these two devices to create a simple sine wave. Use multiple transmitters to amplify the signal's power. You can attach the transmitters to an antenna and send your signal into space.
Create a receiver with a diode, two pieces of wire, a small metal stake and crystal earphones. Simple receivers will probably only get AM stations -- not FM stations.
Find and stand near an AM radio tower. Usually standing within 1.6 km (one mile) of the tower will allow you to get its signal.
Push the stake into the ground and take the insulation off 3 m (10 feet) of the wire. Wrap the wire around the metal stake between five and ten times.
Attach a diode to the end of the ground wire not attached to the stake. Connect the diode to an antenna with 3 m (10 feet) of the wire. Lay the wire on the ground or hang it in a nearby tree; be sure the bare end of the wire is off of the ground.
Connect the leads from the earphones to the diode and put the earphone on your ear. You should hear a signal from the nearby radio tower.