Controlling something remotely often seems a daunting task, requiring either expensive components or a lot of experience with radios and electronics. But it doesn't have to be! Here I show how to easily adapt existing circuits to suit your own needs.
Step 1: Finding a Controller
The easiest way to do this is to find a cheap R/C car at a thrift shop or resale store. If that fails, controllers from one toy can be paired with another, assuming both operate on the same frequency. Note that the controller in this picture is indicated to operate on 27 MHz.
Step 2: Adapting the Controller
If you do not like the controller you have, that's fine. The casing is not terribly important, and the circuit can easily be removed. A simple case which works well for many controllers is an Altoids tin with the inside covered by electrical tape. To protect further against shorts resulting from contact with the metal case, electrical contacts can be covered with hot glue (but keep in mind that some components have a tendency to get warm, especially after prolonged use).
Step 3: Finding a Receiver
This is the circuit board from an R/C car I found broken in a bunch of toys set to be sold at a garage sale. It actually only powered up the one motor you see in the picture, without any steering or other controls. This makes for a relatively boring toy, but a simple circuit. It also meant that receiving a 27 MHz* signal would just apply a voltage across the motor leads, shown with the motor removed in the second picture above.
*If you want this to work, you have to use a transmitter and receiver which both operate on the same frequency (ie: 27 MHz).
Step 4: What Should It Do?
Of course, the motor could be left in place, but assuming you wanted a different function, now is the time to attach something else. Small speakers/buzzers are easy to find, as in this broken toy cell phone I found walking home from school. A "remote detonator" of sorts could be rigged up with a resistive piece of wire; the one shown in the picture heated up to the point where I could no longer touch it in less than a minute (though I would of course not recommend shorting a battery like this). The possibilities are almost endless, with the potential to hook up radio controlled LEDs, solenoids, and just about any other simple electrical device.
Step 5: WARNING
If you do choose to make this, realize that the receiver circuit was designed for a specific purpose. It is only meant to supply a certain amount of power, and swapping out components could potentially damage the circuit (or component) and create a hazard. Over a long period of time, or with heavy use, this failure will become more likely.
In short, if you want a reliable R/C system to use every day, a different (albeit more expensive) setup will better suit your needs. If you need to jerry-rig a warning light to communicate with your friend in the zombie apocalypse, this will better suit your needs.
Have fun with this, be safe, and if you make something inspired by what I've shared here, I would love to see some pictures of it.