that kind of depends on what your doorbell is using quick google seems to suggest anything from 6 volts to 24 volts ac and dc
it may be a couple resistors to drop the 6 volts dc down to 5, it might require a rectifier and some voltage conversion / transistor action, but nothing too serious, few bucks and a little time with solder and wire
you probally would wire it into where the switch returns to the unit, if you look inside theres usually a couple screw terminals that run out to your door and back, find the one thats only has voltage when the button is pressed, have the arduino wait for an input, run its thing and wait for another input (guess you could do it closer to the switch depending on your needs)
I guess my real question is what are you trying to do? if your interfacing with a existing doorbell system then the above holds true, if your got a button but nothing to connect it to, as long as its not too far away you could just use the doorbell switch as a normal switch and have your arduino chime in place.