Cadence is basically just a measurement of frequency or 'counts per second'. So, you'll need:
* Crank magnet and reed switch salvaged from a dead bike computer. Wheel magnet and switches should be usable too if suitably hacked.
* A battery
* A multimeter with a gert big display on it which has a frequency meter as one of its modes. You should be able to find a USB one if you want super pimpy display.
If you were thinking of reaching for the Maplin catalogue, you should be able to work the rest out for yourself. Of course, you'll be getting Hertz – revs per second – not RPM, so you'll have to multiply by 60 in your head…
If you want data logging, there are a lot worse and more expensive ways of doing it than using an Arduino, and you can re-use the hardware in the summer / when you're fit / get bored with turbo training. Or, again, get a USB data logger or oscilloscope or something that will do the job.