The fan example is nice and simple, so I'll go with that.
There are two ways that I think of, right off:
-Use a "dumb" circuit to respond to a signal, e.g. IR signal like a TV remote outputs.
-Create a "smart" (and not nearly as cheap?) circuit via wireless serial port (e.g. Xbees) or bluetooth serial port
I've never really done the former, but I'll describe the latter process...
The fan is nice, because ultimately it's a motor with a power supply. In the simplest case, you would have on/off. I've never taken one apart, so I don't know for sure how the speed control/knob works. I'm mostly a "combine major components" rather than a "build circuits" guy so that's how I'm approaching this.
On the fan end, you would have a microcontroller (cheapest you can find, perhaps, since this is such a simple set of requirements), a motor driver (aka motor controller), and some method of remote control (xbee or bluetooth being most common option here). These devices all need power for the logic circuits (e.g. 5 V from a regulator). The fan's power supply and motor would be connected via the motor driver. The motor driver regulates the speed and polarity of the power being sent to the fan motor. The microcontroller in turn receives input from the xbee/bluetooth, interprets it, and sends the correct commands (actually just PWM signals) to the motor driver.
On your end, you'd have some sort of controller/remote to send the signals to the fan. This could be a computer, or it could be a black box with buttons/knobs, another microcontroller to interpret button presses or knob positions; and the other end of the xbee/bluetooth connection. Also a power supply (battery) for the microcontroller route.
With the components I'm familiar with, the xbee/bluetooth is probably the biggest cost (if you have a computer with bluetooth already, this is $20 or so... otherwise a range of > 30ft will need around $80 in stuff =-x ). The two microcontrollers should be doable for less than $30 (maybe less than $20). The motor driver would be something under $30, but I don't know how much current typical fans draw - higher current motor drivers = more $$.
There'd be a bit of software involved, too, but this would be pretty straight forward (imo) using Webbotlib.
Again, there's other ways and definitely some cheaper ways. I'm just good at solving problems with money, evidently.