The Arduino board is an interface that includes some USB and Serial communication hardware and an oscillator; Basically just a way to easily talk to the main chip, the ATMega328, which is programmed with the Arduino bootloader.
You can get ATMega328 chips with the Arduino bootloader preloaded:
plus a 16Mhz crystal or resonator:
and you'll have a fully functioning "Arduino". If you need to program it, just plug the chip back into an Arduino duemillinove board and upload the code. Here is the diagram for where you would connect your wires:
I hope this helps :)