Have a quick look at my two previous posts-http://forum.arduino.cc/index.php?topic=203425.0
Oregon Scientific WMR86 Weather Station
Bios or Thermor Weather Station (now scrapped)
I had the Bios working for years, and bought one replacement after it clagged. When the last one clagged, I swapped over to Oregon Scientific and decoded it in a similar fashion way (using much information from similar URL references to those that are listed below). Most people seem to approach the problem by counting clock cycles during interrupts which leads to some fancy maths checking upper and lower limits. I have a simpler approach using delays to sample the waveform and see if it conforms to proper Manchester bit encoded data.
If you go down the path of using the analogue inputs of a computer as a cheap CRO (I did in both cases to sort out the initial detail in the waveforms, they had opposite polarity) it is very useful if you can use both channels and sample the 433Mhz with one channel and put out strobes from the Arduino on pin13 to check your timing etc. It can be quite an illuminating debug exercise.
Both posts have working programs, graphics etc. Good luck, it is very satisfying when you have cracked it. The Oregon took me 2 and half weeks (I won't admit to how long it took the Bios, my first, to do). Just buy a 433MHz receiver for a few dollars to put on the Arduino and keep the original receiver on the kitchen shelf. Tapping into the original receiver will not make the whole programming exercise any simpler. If is based on an Oregon, hopefully most of the hard work is done.
PS This was my choice of interrupt timer versions: http://www.lostbyte.com/Arduino-OSV3/ firstname.lastname@example.org