You can't really transmit an analog signal. The Analog signal from a potentiometer is a variable voltage, and you can't transmit a voltage. So you have to have some electronics that transform the voltgae to a signal that can be transmiited (Analog to digital converter = ADC), then have a transmiter with that and a reciever inthe other end with the Arduino board.
One way to do that is to use two arduino boards with blue tooth or some other wirelsess connection between them.
Two arduinos with Bluetooth would certainly do the trick. But if you are on a budget, you could investigate using the pot to control a pulse width connected to a transmitter/receiver pair that can handle the range of frequencies you are sending. Perhaps something like this: RF Link 2400bps Receiver - 315MHz - WRL-08948 - SparkFun Electronics modulated by a 555 timer with pulse rate controlled by the pot.
I haven't done it myself so don't have much more to add, but it may be worth researching if you want to do this on a shoestring. You can find more info on the transmitter at Sparkfun. And there are lots of simple circuits for generating a pulse proportional to pot position using 555s, here is one picked at random: http://www.doctronics.co.uk/555.htm
Others may have better suggestions for more appropriate low cost devices to consider if you want to go this route.
I have a somewhat similar problem as Bowez's , but the scenario is:
I want to replicate my potentiometer in my board in such a way that the job of the potentiometer will replaced by my microcontroller ( Arduino) . I guess I need to build a digital to analog circuit?
Is this the right way? How will I pull this off? Any suggested circuits?
Application: Motor control, When the potentiometer is centered the motor does not turn....Rotating it clockwise makes the motor turn one way...anticlockwise..the other".
Assuming the action of the pot is to change a voltage you can use the PWM output from the arduino to give you a controllable output voltage. You will also need an RC filter.
See:- http://www.thebox.myzen.co.uk/Tutorial/PWM.html
I hope I'm not too late. We have a product that is designed to do exactly what you need. It will sample an analog voltage on one node, transmit wirelessly, and regenerate the voltage on the other node.
We also have a wireless potentiometer example in the documentation, and provide discounts for students or university if cost is a concern. The product is located at http://www.starmanelectric.com.