This toy is a simple radio-controlled vibrating egg. It works in a straightforward manner: The user wears the vibrating egg; a radio control can switch the egg on and off from a distance of about 25 feet.
The first thing to do is get the parts. I used an "egg" type vibrator -- this is just an egg-shaped vibrator attached by two wires to a control and battery pack. It should run on two "AA" batteries. For the radio, go to Radio Shack and find one of their radio-controlled toy cars. The type you'll need is the bottom-of-the-line cheap kind. The transmitter should be a simple push button or trigger (not the kind that uses a steering wheel to control the car's direction!). The car will be one of the ones that runs all the time when the power switch is on--it spins around in a circle in reverse when you push the transmitter button, and goes straight forward when you don't push the button. (The drive wheels spin all the time, and pressing the transmitter button just changes the direction they spin.) The car should also run on two "AA" batteries. These cars usually cost about twelve bucks. While you're there, you'll also need a couple of power diodes--1N4001, 1N4009, or similar (it doesn't really matter too much what kind as long as they're power diodes), and a small "SPDT" (single pole, double throw) toggle switch--it will have three connectors on it.
To build it: First, cut the wires leading to the vibrator at a place close to the battery/control pack. Put the control pack aside and remove the plastic shell from the car. When you have the shell off, remove the wheels, and locate the motor that drives the rear wheels. Carefully cut the two wires that lead from the small circuit board inside the car to the drive motor, as close to the motor as possible. Remove the motor and drive axle. If you have a small saw, you can cut the plastic chassis so all you have left is a circuit board sitting on top of a battery pack. Solder one of the wires that used to go to the car's drive motor to one of the wires that leads to the vibrator. (It doesn't matter which one goes to which one.) Solder the other wire that used to go to the drive motor to the CENTER terminal on the SPDT switch. Now examine the power diodes--there will be a band or stripe painted on the diode close to one end. This end is called the "cathode." Solder the cathode end of one of the diodes to one of the remaining two terminals on the switch. Solder the other end (the "anode") of the other diode to the last terminal on the switch. Take the two ends of the diodes that are free and solder them together, and solder the place where they join to the remaining wire leading to the vibrator.
Testing the unit: Turn on the power to the radio receiver from the car. The vibrator may start running immediately, even without pressing the transmitter button. If it does, flip the SPDT switch to its other position. It should stop, and run only when the transmitter button is pressed.
The switch toggles the way the vibrator runs. In one position, it should run only when the transmitter is activated; in the other position, it will run all the time and stop when the transmitter button is pressed. (This has all kinds of potential uses of its own; use your imagination!)
If it doesn't work, check to make sure: Does the radio control car run on the same voltage as the vibrator (i.e., does it use the same number of batteries)? Are the connections clean and secure? Is the transmitter in range? (Most cars have a "whip" antenna; if you remove this antenna when you disassemble the car, replace it with a piece of wire of the same length.) Check the wires coming from the transmitter: one should go straight to the vibrator; the other should go to the "pole" of the SPDT switch. Are the diodes connected properly? The cathode end of one should be attached to the anode of the other; the place where they join should go to the vibrator; one end of each diode should be attached to an outer terminal of the switch. Diodes are damaged by excessive heat; use care when soldering them, and if you have one, attach a clip heatsink to the wires going to the diodes while soldering. (If you solder them carefully, they'll be okay.)
If you want to get fancy, you can use a small plug (I used a phono plug) to connect the vibrator to the receiver, instead of soldering them together. That way, you can attach the proper plug to the battery pack that used to be connected to the vibrator, and use it both ways.