The idea here is you have a Methane sensor that smells a fart, then sends a high signal to an Arduino that picks a random number (which will be your new TV channel) and then sends the correct light pulses to an Infrared LED to change the channel. So to do that I'm going to break up the components list into two parts. Part One is all set up components and Part Two is stuff that's actually going to be a permanent part of the project.
Arduino (I use a Duemilanove... $30-$35 depending on where you buy it. I bought mine from Make: as part of a kit http://www.makershed.com/ProductDetails.asp?ProductCode=MSGSA
which comes with a Tactile Switch. But a cheaper option might be to go to Spikenzie Labs and buy an Arduino/Switch combo from them http://www.spikenzielabs.com/Catalog/index.php?main_page=product_info&cPath=12&products_id=40
is the Arduino and the switch is linked lower)
Prototyping shield ($12.50)
1/4-Size Breadboard ($4)
(Or you could replace the ProtoShield and 1/4-Size breadboard with a solderless breadboard)
1X Working TV with,
1X Working TV remote
Part One Components:
1X 10K Ohm 1/4Watt resistor ($0.99 for a 5 pack)
1X 100 Ohm 1/4Watt resistor ($0.99 for a 5 pack)
5X 15 Ohm 1/2Watt resistors ($0.99 for a 5 pack)
1X Momentary Tactile Pushbutton Switch ($0.35)
1X 38kHz Infrared Receiver Module ($3.95)
Part Two Components:
1X CH4 Methane Sensor ($29.99)
1X Infrared LED ($1.99)
(Some of the resistors from Part One; I'll explain this in a later step)
1X Plastic Enclosure (RadioShack sells them, but I was going to use one I picked up at Fry's a while back)
1X 9V battery and battery holder
Multimeter (for calibrating your CH4 Methane Sensor)
So if you're starting from scratch you're looking at about USD$86.00. I'm guessing most folks on this site and looking at this 'Ible already have the tools, Arduino and ProtoShield which would put the cost around USD$40.00 (A $34.00 CH4 Methane Sensor/IR Receiver Parallax order and a trip to RadioShack for resistors/IR LED).
Sketches are linked on the steps that they are used in. I did my best to document and put notes into my code but I'll be happy to explain anything that isn't clear. Just ask.